




Courses

Linear Algebra(SPRING_2018)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
 • Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)
 • Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix
 • Introduction to Matrices 2( symmetric/ skewsymmetric/ orthogonal/ conjugate/ hermitian/ skewhermitian/ normal/ unitary matrices, matrix norm, positive/negative (semi)definite matrices, quadratic form, Silvester criterion)
 • Linear equations1 (Homogeneous system, Augmented matrix, inconsistency, illcondition, condition number, Gaussian elimination, Backward substitution algorithm, Elementary matrix, Elementary matrix ,
 • Linear equations2 ( Gauss Jordan, Row echelon form, pivoting, reduced row echelon form, LU factorization, LU factorization with pivoting, Cholesky factorization) , Applications of linear systems in network analysis, electrical circuits and chemical equations, polynomial interpolation, economics (Leontief InputOutput Models)
 • Vector spaces ( Field & vector space, subspace, Linear combination, Column/Row space, Spanning sets, linear independency, Basis, Dimension, Rank, Coordinate, Range space, Null space, Nullity, Fundamental subspaces)
 • Linear transformation ( functions, onetoone function, surjective (onto) function, function composition, Matrix functions, identity and inverse transformation, Linear transformation, matrix linear transformations, linear transformation null space and range space, rank and nullity of a linear transformation, Isomorphism, Similar matrices, Similarity transformation)
 • Eigenvalues and eigenvectors (Eigenvalues, Eigenvectors, Characteristic equation, Monic, CayleyHamilton theorem , Power method, QR factorization, Diagonal form, Block diagonal form, Companion form, Jordan canonical form, minimal polynomial, Applications (Markov chain, Differential equations)
 Inner product vector spaces, orthogonality, Leastsquare problem (inner product spaces, Orthogonal complement, Orthogonal basis, Orthonormal basis, GramSchmidth process, Orthogonal projection, Least square problem, Normal equations, QR factorization, Cholesky factorization), mathematical modelling using least squares, Function approximation (fourier series)
 • Singular value decomposition (Singular values, Singular value decomposition (SVD), left and right singular vectors, rank/ 2norm/ determinant/ inverse matrix computation based on SVD, Pseudoinverse), ,Applications (Data compression, PCA algorithm)
 • Matrix polynomials & functions (Matrix polynomials, Matrix functions, inverse matrix computation, Statespace representation, Similar realizations, State transition matrix, methods for computation of state transition matrix)
Text Book:
 جبر خطي ، سيمور ليپشوتس، مارک ليپسون، ترجمه دكتر علي اکبر محمدي حسن آبادي، انتشارات نوپردازان، 1391

Linear Algebra(SPRING_2018)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
 • Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)
 • Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix
 • Introduction to Matrices 2( symmetric/ skewsymmetric/ orthogonal/ conjugate/ hermitian/ skewhermitian/ normal/ unitary matrices, matrix norm, positive/negative (semi)definite matrices, quadratic form, Silvester criterion)
 • Linear equations1 (Homogeneous system, Augmented matrix, inconsistency, illcondition, condition number, Gaussian elimination, Backward substitution algorithm, Elementary matrix, Elementary matrix ,
 • Linear equations2 ( Gauss Jordan, Row echelon form, pivoting, reduced row echelon form, LU factorization, LU factorization with pivoting, Cholesky factorization) , Applications of linear systems in network analysis, electrical circuits and chemical equations, polynomial interpolation, economics (Leontief InputOutput Models)
 • Vector spaces ( Field & vector space, subspace, Linear combination, Column/Row space, Spanning sets, linear independency, Basis, Dimension, Rank, Coordinate, Range space, Null space, Nullity, Fundamental subspaces)
 • Linear transformation ( functions, onetoone function, surjective (onto) function, function composition, Matrix functions, identity and inverse transformation, Linear transformation, matrix linear transformations, linear transformation null space and range space, rank and nullity of a linear transformation, Isomorphism, Similar matrices, Similarity transformation)
 • Eigenvalues and eigenvectors (Eigenvalues, Eigenvectors, Characteristic equation, Monic, CayleyHamilton theorem , Power method, QR factorization, Diagonal form, Block diagonal form, Companion form, Jordan canonical form, minimal polynomial, Applications (Markov chain, Differential equations)
 Inner product vector spaces, orthogonality, Leastsquare problem (inner product spaces, Orthogonal complement, Orthogonal basis, Orthonormal basis, GramSchmidth process, Orthogonal projection, Least square problem, Normal equations, QR factorization, Cholesky factorization), mathematical modelling using least squares, Function approximation (fourier series)
 • Singular value decomposition (Singular values, Singular value decomposition (SVD), left and right singular vectors, rank/ 2norm/ determinant/ inverse matrix computation based on SVD, Pseudoinverse), ,Applications (Data compression, PCA algorithm)
 • Matrix polynomials & functions (Matrix polynomials, Matrix functions, inverse matrix computation, Statespace representation, Similar realizations, State transition matrix, methods for computation of state transition matrix)
Text Book:
 جبر خطي ، سيمور ليپشوتس، مارک ليپسون، ترجمه دكتر علي اکبر محمدي حسن آبادي، انتشارات نوپردازان، 1391

Robust Control(SPRING_2018)
Aims:
In this course the concept of structured and unstructured model uncertainties in system model are introduced and stability and performance analysis of feedback system in the presence of model uncertainty is discussed. Also, robust synthesis methods of H? controllers and ?analysis for uncertain systems are introduced
Syllabus:
 کاهش مدل ( تحقق متوازن، روش برش متوازن، کاهش مرتبه کنترل کننده)
 Overview of robust control
 Introduction on linear algebra & linear dynamical systems
 Linear spaces, Innerproduct spaces, Hilbert spaces, Banach spaces, H_2 and H_infinity spaces, norms of signals and systems, Relation between signals and systems norm, Computing H_2 and H_infinity norms, Frequencydomain interpretation of H_infinity norm, Timedomain interpretation of H_infinity norm
 Internal stability, Wellposedness, Coprime Factorization, Plant factorization, Coprime Factorization of a stabilizing controller
 Performance Specifications, Feedback properties, performance tradeoffs & design limitations, sensitivity transfer matrices, Weighted H_2 & H_? problems, H_2& H_? mixedsensitivity, analyticity or interpolation conditions, waterbed effect.
 Modeling uncertainty and robustness, representation of uncertainties, structured and unstructured uncertainties, parameterized, additive and multiplicative uncertainties, Robust Stability, Robust Performance, Smallgain Theorem , Robustness for Unstructured Uncertainties
 Linear Fractional Transformation (LFT), Formulation of control problems in LFT framework, parameterization of all stabilizing controller,
 mu synthesis, structured singular value, structured robust stability, robust performance
 Algebraic Riccati Equations (AREs), stabilizing solutions for ARE, Bounded Real Lemma (BRL)
 H_infinity control problem
 Introduction to convex optimization, introduction to Linear Matrix Inequalities (LMIs), application of LMIs in H_2 & H_infinity optimal control problems
Text Book:
 K. Zhou and J. Doyle, "Essentials of robust control", Prentice Hall, 1998

Advanced Topics in Multi Agent Systems(FALL_2017)
Aims:
In this course, analysis and synthesis methods are discussed for distributed controller design in multiagent systems. Also, the effect of switching interaction topologies, timedelays and measurement noises are investigated in such systems
Syllabus:
 Introduction to multiagent systems: Definitions, Motivations, Characteristics, Applications,
 Introduction to algebraic graph theory and stochastic matrix theory
 Distributed consensus protocols
 Containment control
 Flocking algorithms
 Timedelay in multiagent systems
 Consensus in stochastic setting
 Measurement and noise analysis in multiagent systems
 Optimal cooperative control
 Eventtriggered control for multiagent systems
Text Book:
 Distributed Coordination of Multiagent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, SpringerVerlag, London, 2011
 Distributed Consensus in MultiVehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, SpringerVerlag, London, 2008

Electric Circuits (II)(FALL_2017)
Aims:
Study of a systematic approach to the analysis of the complex networks , Laplace transform and its application in circuit analysis
Syllabus:
 Network Graphs and Tellegen’s Theorem
 Node and Mesh Analysis
 Loop and Cutset Analysis
 State Equations
 Laplace Transforms
 Natural Frequencies
 Network Functions
 Network Theorems
 Twoports
Text Book:
 Charles A.Deseor and Ernest s.Kuh, Basic Circuit Theory, Mc Graw Hill, 1969
 James W. Nilson, Electric Circuits (4th edition), Addison Wesley, 1990

Linear Algebra(FALL_2017)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
 • Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)
 • Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix
 • Introduction to Matrices 2( symmetric/ skewsymmetric/ orthogonal/ conjugate/ hermitian/ skewhermitian/ normal/ unitary matrices, matrix norm, positive/negative (semi)definite matrices, quadratic form, Silvester criterion)
 • Linear equations1 (Homogeneous system, Augmented matrix, inconsistency, illcondition, condition number, Gaussian elimination, Backward substitution algorithm, Elementary matrix, Elementary matrix ,
 • Linear equations2 ( Gauss Jordan, Row echelon form, pivoting, reduced row echelon form, LU factorization, LU factorization with pivoting, Cholesky factorization) , Applications of linear systems in network analysis, electrical circuits and chemical equations, polynomial interpolation, economics (Leontief InputOutput Models)
 • Vector spaces ( Field & vector space, subspace, Linear combination, Column/Row space, Spanning sets, linear independency, Basis, Dimension, Rank, Coordinate, Range space, Null space, Nullity, Fundamental subspaces)
 • Linear transformation ( functions, onetoone function, surjective (onto) function, function composition, Matrix functions, identity and inverse transformation, Linear transformation, matrix linear transformations, linear transformation null space and range space, rank and nullity of a linear transformation, Isomorphism, Similar matrices, Similarity transformation)
 • Eigenvalues and eigenvectors (Eigenvalues, Eigenvectors, Characteristic equation, Monic, CayleyHamilton theorem , Power method, QR factorization, Diagonal form, Block diagonal form, Companion form, Jordan canonical form, minimal polynomial, Applications (Markov chain, Differential equations)
 Inner product vector spaces, orthogonality, Leastsquare problem (inner product spaces, Orthogonal complement, Orthogonal basis, Orthonormal basis, GramSchmidth process, Orthogonal projection, Least square problem, Normal equations, QR factorization, Cholesky factorization), mathematical modelling using least squares, Function approximation (fourier series)
 • Singular value decomposition (Singular values, Singular value decomposition (SVD), left and right singular vectors, rank/ 2norm/ determinant/ inverse matrix computation based on SVD, Pseudoinverse), ,Applications (Data compression, PCA algorithm)
 • Matrix polynomials & functions (Matrix polynomials, Matrix functions, inverse matrix computation, Statespace representation, Similar realizations, State transition matrix, methods for computation of state transition matrix)
Text Book:
 جبر خطي ، سيمور ليپشوتس، مارک ليپسون، ترجمه دكتر علي اکبر محمدي حسن آبادي، انتشارات نوپردازان، 1391

Linear Algebra(SPRING_2017)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
 • Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)
 • Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix
 • Introduction to Matrices 2( symmetric/ skewsymmetric/ orthogonal/ conjugate/ hermitian/ skewhermitian/ normal/ unitary matrices, matrix norm, positive/negative (semi)definite matrices, quadratic form, Silvester criterion)
 • Linear equations1 (Homogeneous system, Augmented matrix, inconsistency, illcondition, condition number, Gaussian elimination, Backward substitution algorithm, Elementary matrix, Elementary matrix ,
 • Linear equations2 ( Gauss Jordan, Row echelon form, pivoting, reduced row echelon form, LU factorization, LU factorization with pivoting, Cholesky factorization) , Applications of linear systems in network analysis, electrical circuits and chemical equations, polynomial interpolation, economics (Leontief InputOutput Models)
 • Vector spaces ( Field & vector space, subspace, Linear combination, Column/Row space, Spanning sets, linear independency, Basis, Dimension, Rank, Coordinate, Range space, Null space, Nullity, Fundamental subspaces)
 • Linear transformation ( functions, onetoone function, surjective (onto) function, function composition, Matrix functions, identity and inverse transformation, Linear transformation, matrix linear transformations, linear transformation null space and range space, rank and nullity of a linear transformation, Isomorphism, Similar matrices, Similarity transformation)
 • Eigenvalues and eigenvectors (Eigenvalues, Eigenvectors, Characteristic equation, Monic, CayleyHamilton theorem , Power method, QR factorization, Diagonal form, Block diagonal form, Companion form, Jordan canonical form, minimal polynomial, Applications (Markov chain, Differential equations)
 Inner product vector spaces, orthogonality, Leastsquare problem (inner product spaces, Orthogonal complement, Orthogonal basis, Orthonormal basis, GramSchmidth process, Orthogonal projection, Least square problem, Normal equations, QR factorization, Cholesky factorization), mathematical modelling using least squares, Function approximation (fourier series)
 • Singular value decomposition (Singular values, Singular value decomposition (SVD), left and right singular vectors, rank/ 2norm/ determinant/ inverse matrix computation based on SVD, Pseudoinverse), ,Applications (Data compression, PCA algorithm)
 • Matrix polynomials & functions (Matrix polynomials, Matrix functions, inverse matrix computation, Statespace representation, Similar realizations, State transition matrix, methods for computation of state transition matrix)
Text Book:
 جبر خطي ، سيمور ليپشوتس، مارک ليپسون، ترجمه دكتر علي اکبر محمدي حسن آبادي، انتشارات نوپردازان، 1391

Robust Control(SPRING_2017)
Aims:
In this course the concept of structured and unstructured model uncertainties in system model are introduced and stability and performance analysis of feedback system in the presence of model uncertainty is discussed. Also, robust synthesis methods of H? controllers and ?analysis for uncertain systems are introduced
Syllabus:
 Overview of robust control
 Introduction on linear algebra & linear dynamical systems
 Linear spaces, Innerproduct spaces, Hilbert spaces, Banach spaces, H_2 and H_infinity spaces, norms of signals and systems, Relation between signals and systems norm, Computing H_2 and H_infinity norms, Frequencydomain interpretation of H_infinity norm, Timedomain interpretation of H_infinity norm
 Internal stability, Wellposedness, Coprime Factorization, Plant factorization, Coprime Factorization of a stabilizing controller
 Performance Specifications, Feedback properties, performance tradeoffs & design limitations, sensitivity transfer matrices, Weighted H_2 & H_? problems, H_2& H_? mixedsensitivity, analyticity or interpolation conditions, waterbed effect.
 Modeling uncertainty and robustness, representation of uncertainties, structured and unstructured uncertainties, parameterized, additive and multiplicative uncertainties, Robust Stability, Robust Performance, Smallgain Theorem , Robustness for Unstructured Uncertainties
 Linear Fractional Transformation (LFT), Formulation of control problems in LFT framework, parameterization of all stabilizing controller,
 mu synthesis, structured singular value, structured robust stability, robust performance
 Algebraic Riccati Equations (AREs), stabilizing solutions for ARE, Bounded Real Lemma (BRL)
 H_infinity control problem
 Introduction to convex optimization, introduction to Linear Matrix Inequalities (LMIs), application of LMIs in H_2 & H_infinity optimal control problems
 کاهش مدل ( تحقق متوازن، روش برش متوازن، کاهش مرتبه کنترل کننده)
Text Book:
 K. Zhou and J. Doyle, "Essentials of robust control", Prentice Hall, 1998

Advanced Topics in Multi Agent Systems(FALL_2016)
Aims:
In this course, analysis and synthesis methods are discussed for distributed controller design in multiagent systems. Also, the effect of switching interaction topologies, timedelays and measurement noises are investigated in such systems
Syllabus:
 Introduction to multiagent systems: Definitions, Motivations, Characteristics, Applications, Distributed control categorization, Emergent issues
 Introduction to algebraic graph theory: Preliminaries, Graph Laplacian, Eigenstructure of graph Laplacian, nonnegative matrices, ergodic (SIA) matrices, scrambling matrices, Mmatrix
 Distributed consensus protocols: Firstorder consensus protocols (Fixed topology/Switching topology, Continuoustime/Discretetime), Leaderfollowing case (Constant reference state, Timevarying reference state), Secondorder consensus protocols (Fixed topology/Switching topology, Bounded control input, No state derivative measurements, With group reference velocity/Partial access to a group reference state, Secondorder consensus with sampled data
 Containment control: Definitions, Applications, Multiple Stationary Leaders (Directed Fixed Interaction, Directed Switching Interaction), Multiple Dynamic Leaders (Directed Fixed Interaction, Directed Switching Interaction)
 Flocking algorithms:Flocking algorithm without group objective, Leaderfollowing flocking algorithm,Flocking algorithm with obstacle avoidance, Flocking with a minority of informed agents, Connectivitypreserving flocking algorithm, Connectivitypreserving flocking algorithm with bounded potential function, Adaptive flocking algorithms with nonlinear dynamics
 Timedelay in multiagent systems:Basic definitions, Types of timedelays in multiagent systems, Analysis techniques (Frequencydomain techniques, Techniques based on Lyapunovkrasovaskii function (LMI tool), Techniques based on Stochastic matrix theory), synthesis and analysis of delayed consensus protocols in switching networks (with timevarying delays)
 Stochastic setting:An overview on random variables, Stochastic version of LaSalle’s Theorem, Consensus definitions in stochastic setting, Consensus over random graph (Undirected edges with the same probability and the same weight, Directed edges with the different probabilities and different positive weights, Nonexpansive and pseudocontractive matrices, Directed edges with the different probabilities and different arbitrary weights)
 Measurement and communication noise:An overview on stochastic processes, Gaussian or normal process, Stationary Process, The concept of white noise, Process with independent increments, The Wiener process, Stochastic differential equations, Itô Rules, continuoustime mean square averageconsensus (with measurement noises, with measurement noises and timevarying communication timedelays, with measurement noises and arbitrary switching topology
Text Book:
 1 Distributed Coordination of Multiagent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, SpringerVerlag, London, 2011.
 2 Distributed Consensus in MultiVehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, SpringerVerlag, London, 2008.

Modern Control(FALL_2016)
Aims:
In this course, modelling and designing the control systems are investigated in state space
Syllabus:
 1 Introduction to modern control systems: Control system definition, Control system physical components, Control system conceptual components, Controller designing procedure, Advantages of state space representation over transfer function representation
 Introduction to linear algebra and matrix analysis: Vector space, Linear combination, Change of basis and coordinates in Ndimensional space, Linear transformation, Determinant, Eigenvalues and eigenvectors, Jordan canonical form, Matrix functions
 Linear systems representation: State space representation, system modelling based on physical principles, system modelling based on Lagrangian method, Linearization of Nonlinear differential equations, inputoutput representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Timedomain solution of LTI state equations
 computing methods for state transition matrix (Laplace method, CaleyHamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Blockdiagonal form, System dynamic modes, Modal decomposition, solution of LTI system to exponential input
 Controllability and observability: necessary and sufficient conditions for controllability, necessary and sufficient conditions for observability, Canonical Jordan form test method, Unstable polezero cancellation, Uncontrollable and unobservable systems decomposition, Kalman decomposition
 Realization theory : Minimal Realization (definitions and conditions), Realization of SISO systems (Controllable canonical form, Observable canonical form, Jordan canonical realization, Parallel and serial realization), Realization of MIMO systems, Realization of MISO systems, Realization of SIMO systems
 Stability: Definitions (Lyapunov stability, Asymptotically stability, Global asymptotically stability, BIBO stability, Internal stability), stability in LTI systems, stability of Nonlinear systems ( linearization method, Lyapunov method)
 Linear Timevarying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Timevarying realization, internal stability for LTV systems
 State feedback: state feedback controller design in SISO systems, state feedback gain (Bass and Gura method, Ackerman method, Controllable canonical realization method, state feedback effect on controllability and observability, state feedback effect on system zeros, state feedback for uncontrollable systems, state feedback design for multivariable systems
 State estimator (State observer): fullorder observer, Reducedorder observer, State feedback based controller with fullorder observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reducedorder observer
Text Book:
 CT Chen, Linear System Theory and Design, 3rd edition, Oxford Universiy Press, 1999
 علي خاكي صديق، اصول كنترل مدرن، انتشارات دانشگاه تهران، 1383












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