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
Same as Reference
References
1. Applied nonlinear Control, Jean‐ Jacques Slotine and Weiping Li, Prentice Hall, ISBN:0‐13‐040890, 1991.
2. Nonlinear Systems, H.K. Khalil, 3rd ed., Prentice hall, 2002.
3. Bilinear Systems, D. Elliott, Springer, 2009.
4. Nonlinear Systems; Analysis, Stability and Control, Shankar Sastry, Springer. 1999.
5. Stability by Liapunov's direct method: with applications, P. LaSalle, Solomon Lefschetz Joseph Academic Press, 1961.
6. Nonlinear systems analysis, Mathukumalli Vidyasagar, SIAM, 2002.
Course Outcomes (COs):
CO1: Explain the role of nonlinear elements in control systems and provide an overview of methods used for their analysis.
CO2: Describe the concepts of phase plane analysis and apply them to both linear and nonlinear systems.
CO3: Utilize Lyapunov's direct method and invariant set theorems to assess stability and instability of nonlinear systems.
CO4: Extend stability concepts to non-autonomous systems and apply Lyapunov analysis techniques.