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Course Contents

Norms of Signals, Vectors and Matrices, Positive Definite Functions, Positive Definite Matrices; Continuous time State space Model, L TI State space Model, Nonlinear State space model, Equilibrium point and Linearization using first order Taylor series, Linearization technique for operating points other than origin; Lyapunov Stability Theory, Lyapunov stability of time invariant system, LaSalle's Invariance Theorem, Chetaev's Instability Theorem, Lyapunov stability of time varying system, Lyapunov's indirect method, Lyapunov stability for linear systems; Discrete time Systems, Discrete time L TI State space Model, Discrete time Nonlinear State space model, ARMAX and NARMAX Models, Lyapunov Stability for Discrete Time Systems; Modeling of Different Nonlinear Systems: Inertial Wheel Pendulum, Two Link Manipulator, Inverted Pendulum Mounted on A Cart, Induction Motor; Nonlinear Control Strategies: Feedback Linearization, Back stepping Design, State feedback linearizable systems. Feed Forward Networks: Multilayered Neural Networks, Radial Basis Function Networks. Adaptive Learning Rate; Feedback Networks, Back Propagation Through Time (BPTT), Real Time Recurrent Learning (RTRL); Kohonen Self Organizing Map; System Identification Using Neural Networks Classical sets, Fuzzy Sets, Concept of a fuzzy number, Operations on Fuzzy sets, Properties of Fuzzy Sets, Some Typical Membership Functions; Extension Principle of Fuzzy Sets, Crisp Relation, Fuzzy Relations, Projection of Fuzzy Relations, Cylindrical Extension of Fuzzy Relations, Relation Inference; Fuzzy Rule Base and Approximate Reasoning, Fuzzy Linguistic Variables, Linguistic modifier, Rule base systems, Fuzzy Rule base, Fuzzy Implication Relations, Fuzzy Compositional Rules, Inference mechanism compared, Approximate Reasoning; Fuzzy Logic Control (FLC), Mamdani Model, Takagi Sugeno {TS) Fuzzy Model; System Identification Using TS Fuzzy Models, The TS Model From Input Output Data, The TS Fuzzy Model Using Linearization. 

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