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  • 2:59 PM, Friday, 29 Mar 2024


Course Postgraduate
Semester Sem. I
Subject Code AVC612
Subject Title Nonlinear Dynamical Systems

Syllabus

Introduction to Nonlinear systems: Non-linear elements in control systems, overview of analysis methods.

Phase plane analysis: Concepts of phase plane analysis, Phase plane analysis of linear and nonlinear systems, Existence of limit cycles.

Fundamentals of Liapunov theory: Nonlinear systems and equilibrium points, Concepts of stability, Linearization and local stability, Lyapunov’s direct method, Invariant set theorems,

Lyapunov analysis of LTI systems, Krasovskii’s method, Variable gradient method, Physically motivated Lyapunov functions.

Advanced stability theory: Concepts of stability for Non‐autonomous systems, Lyapunov analysis of non-autonomous systems, instability theorems, Existence of Lyapunov functions, Barbalat’s Lemma and stability analysis.

Text Books
  1. Jean‐ Jacques Slotine and Weiping Li, Applied nonlinear Control, Prentice Hall,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: with applications, Joseph Academic Press, 1961
  6. Mathukumalli Vidyasagar, Nonlinear syste.ms analysis, SIAM, 2002.

 

References

Same as Textbooks