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  • 11:27 AM, Sunday, 24 Oct 2021

Course Postgraduate
Semester Electives
Subject Code AVC 622
Subject Title Non


Introduction: Nonlinear system behavior, Nonlinear control.

Nonlinear system analysis: Phase plane analysis: Concepts of phase plane analysis, Phase plane analysis of linearand nonlinear systems, Existence of limit cycles.

Fundamentals of Lyapunov theory: Nonlinear systems and equilibrium points, Conceptsof stability, Linearization and local stability, Lyapunov’s direct method, Invariant settheorems, Lyapunov analysis of LTI systems, Krasovskii’s method, Variable gradientmethod, Physically motivated Lyapunov functions, Performance analysis. Control designbased on Lyapunov’s direct method.

Advanced stability theory: Concepts of stability for Non-autonomous systems,Lyapunov analysis of non-autonomoussystems, instability theorems, Existence ofLyapunov functions, Barbalat’s Lemma and stability analysis, Positive real systems: PRand SPR Transfer functions, The Kalman-Yakubovich Lemma.

The passivity Formalism: passivity in linear systems., Absolute stability, Establishing boundedness of signals,Existence and Unicity of solutions.

Nonlinear Control systems design: Feedback Linearization and the canonical form, Input-state Linearization of SISOsystems, Input-output Linearization of SISO systems, multi input systems.

Sliding Control: Sliding surfaces, Filippov’s construction of the equivalent dynamics, directimplementations of switching control laws, Continuous approximations of switchingcontrol laws, modeling and performance trade-offsLie derivative, Lie Bracket, Backstepping method for non-feedback linearizable systems

Text Books

1.Jean-Jacques Slotine and Weiping Li, Applied nonlinear Control, PrenticeHall,1991, ISBN: 0-13-040890.

2.H.K. Khalil, Nonlinear Systems, 3rd ed., Prentice hall, 2002.

3.D. Elliott, Bilinear Systems, Springer, 2009.

4.Shankar Sastry, Nonlinear Systems; Analysis, Stability and Control, Springer. 1999.

5.P. LaSalle, Solomon Lefschetz, Stability by Liapunov's direct method: withapplications, Joseph Academic Press, 1961.

6.Mathukumalli Vidyasagar, Nonlinear analysis, SIAM, 2002.

7.Alberto Isidori, Nonlinear Control Systems -Volume 1, Springer, 1995.

8.Alberto Isidori, Nonlinear Control Systems Volume 2, Springer, 1999