**EE 250 CONTROL SYSTEM ANALYSIS**

Continuous and discrete time signals, Fourier series, Fourier, Laplace and Z transform techniques; DFT. Sampling Theorem. LTI systems: I/O description, impulse response and system functions, pole/ zero plots, FIR and IIR systems. Analog and digital filters. Networks: topological description, network theorems, Two port analysis.**EE 451 ADVANCED CONTROL SYSTEMS**

Modeling of physical systems, Concepts of state, state-space, Controllability and observability. Sensitivity and error analysis. Nonlinear systems, singular points, phase plane analysis, Lyapunov stability, describing functions, on-off and dual mode systems. Sampled Data Systems. Computer control system.**EE 455 TRANSDUCERS AND INSTRUMENTATION**

Measurement process; scales of measurement; configuration and functional description of measurement systems; performance characteristics; sensing elements and transducers for measurement of motion, force, pressure, flow, temperature, light, vacuum, etc.; transducer interfacing; signal conditioning, transmission and recording; microprocessor based instrumentation

**EE 650 BASICS OF MODERN CONTROL SYSTEMS**

. Advanced protective relaying, basic protection schemes, relay terminology, Vector spaces, Linear systems, similarity transformations, Canonical forms, Controllability, Observability, Realisability etc. Minimal realization, Digital systems, Nonlinear systems, Phase-plane analysis, Poincare theorems, Lyapunov theorem, Circle and Popov criterion; Robust control, Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, Loop Transfer Recovery (LTR), Hinfinity control.**EE 651 NONLINEAR SYSTEMS**

Describing function, phase-plane analysis. Poincare's Index, Bendixson's theorem. Linearization. Lyapunov stability, stability theorems, variable-gradient technique,and Krasovskii's method for generating Lyapunov functions, statement of Lure problem, circle criterion, Popov criterion, input-output stability.**EE 652 LINEAR STOCHASTIC DYNAMICAL SYSTEMS**

Wiener processes; Markov chains & processes; Filtering, prediction & smoothing. Least squares, Minimum variance, ML and Minimax estimates, error bounds. Kalman and Wiener filters. Optimal control in presence of uncertainty, Synthesis of regulators and terminal controllers, Effect of noisy components on optimal control law. Partially characterised systems.**EE 653 DIGITAL CONTROL**

Discrete-time signals and systems, Z-transform, pulse transfer functions. Compensator design by root locus, error coefficients and frequency response. State-space models of discrete time systems, controllability, observability, stability, state estimation, Kalman filtering. Linear regulation. Parameter estimation.**EE 654 ROBUST CONTROL SYSTEMS**

Linear Quadratic Regulators: return ratio & difference, sensitivity function. Kalman's optimality condition. Gain/phase margins, robustness to time delay and nonlinearity. Characterization of sensitivity. Kharitonov theorem robustness. Singular values - properties, application in stability, robustness and sensitivity. Robustness of discrete time LQR systems.**EE 655 OPTIMAL CONTROL**

Basic mathematical concepts. Conditions for optimality, variational calculus approach, Pontryagin's maximum principle and Hamilton Jacobi-Bellman theory. Structures and properties of optimal systems. Various types of constraints; singular solutions. Minimum time problems.**EE 656 CONTROL SYSTEM DESIGN**

Linear multivariable control systems. Equivalence of internal and external stability of feedback control systems and the stabilization problem. Stable factorization approach for solving stabilization problem. Feedback system design. Solutions of H2 and Ha problems. Robust stabilization, graph topology and graph metric.**EE 637 MATHEMATICAL METHODS IN CONTROL SYSTEMS**

Real and complex Euclidean spaces, Infinite dimensional inner product, complete spaces, Linear functionals and operators, Eigenvalues and eign vectors, complete, orthogonal representations, Errors solutions to systems of linear equations, Matrix inversion, pivoting eigenvalue and eigen vector calculations, SVD, Non linear equations, probability theory, concepts, random variables, distribution functions, moments and statistics of multiple variables, MS estimations, stochastic processes.**EE 658 FUZZY SET, LOGIC & SYSTEMS AND APPLICATIONS**

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).

#### Courses Offered to PG Students

**EE 650 BASICS OF MODERN CONTROL SYSTEMS**

Advanced protective relaying, basic protection schemes, relay terminology, Vector spaces, Linear systems, similarity transformations, Canonical forms, Controllability, Observability, Realisability etc. Minimal realization, Digital systems, Nonlinear systems, Phase-plane analysis, Poincare theorems, Lyapunov theorem, Circle and Popov criterion; Robust control, Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, Loop Transfer Recovery (LTR), Hinfinity control.**EE 658 FUZZY SET, LOGIC & SYSTEMS AND APPLICATIONS**

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).

**EE 658 FUZZY SET, LOGIC & SYSTEMS AND APPLICATIONS**

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).**EE 617 INDUSTRIAL AUTOMATION & CONTROL****EE 671 NEURAL NETWORKS****EE698Y INTELLIGENT INFORMATICS**

**EE 650 BASICS OF MODERN CONTROL SYSTEMS**

Advanced protective relaying, basic protection schemes, relay terminology, Vector spaces, Linear systems, similarity transformations, Canonical forms, Controllability, Observability, Realisability etc. Minimal realization, Digital systems, Nonlinear systems, Phase-plane analysis, Poincare theorems, Lyapunov theorem, Circle and Popov criterion; Robust control, Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, Loop Transfer Recovery (LTR), Hinfinity control.**EE 654 ROBUST CONTROL SYSTEMS**

Linear Quadratic Regulators: return ratio & difference, sensitivity function. Kalman's optimality condition. Gain/phase margins, robustness to time delay and nonlinearity. Characterization of sensitivity. Kharitonov theorem robustness. Singular values - properties, application in stability, robustness and sensitivity. Robustness of discrete time LQR systems.**EE 658 FUZZY SET, LOGIC & SYSTEMS AND APPLICATIONS**

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).**EE 680 INTELLIGENT INSTRUMENTATION****EE 698 CONTROL OF CHAOS**

**EE 658 FUZZY SET, LOGIC & SYSTEMS AND APPLICATIONS**

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).**EE 617 INDUSTRIAL AUTOMATION & CONTROL****EE 671 NEURAL NETWORKS****EE698Y INDUSTRIAL INSTRUMENTATION FOR PROCESS CONTROL**

**EE 654 ROBUST CONTROL SYSTEMS**

Linear Quadratic Regulators: return ratio & difference, sensitivity function. Kalman's optimality condition. Gain/phase margins, robustness to time delay and nonlinearity. Characterization of sensitivity. Kharitonov theorem robustness. Singular values - properties, application in stability, robustness and sensitivity. Robustness of discrete time LQR systems.**EE 653 DIGITAL CONTROL**

Discrete-time signals and systems, Z-transform, pulse transfer functions. Compensator design by root locus, error coefficients and frequency response. State-space models of discrete time systems, controllability, observability, stability, state estimation, Kalman filtering. Linear regulation. Parameter estimation.**EE 705 INTELLIGENT SYSTEMS & CONTROL**

**EE 617 INDUSTRIAL AUTOMATION & CONTROL****EE 671 NEURAL NETWORKS****EE 698B CONTROL OF CYBER PHYSICAL SYSTEMS****EE 698C CONSENSUS IN DISTRIBUTED MULTIAGENT SYSTEM**