Course Content/ Syllabus
Introduction: state-space representation of dynamical systems, phase-portraits of second
order systems, types of equilibrium points; Existence and uniqueness of solutions; Features of
nonlinear dynamical systems; Stability analysis: Lyapunov stability of autonomous systems,
Lyapunov theorem of stability, LaSalle invariance principle, input/output stability of non-
autonomous systems, passivity theorem, small gain theorem, Kalman-Yakubovich-Popov
lemma, Aizermann conjecture, circle/Popov criteria; Limit cycles: Bendixson criterion,
Poincare-Bendixson criterion; Describing functions method, methods of integral quadratic
constraints; Introduction to manifolds.
Texts: (Format: Authors, Book Title in Italics font, Volume/Series, Edition Number, Publisher,
1. H. K. Khalil, Nonlinear systems, Prentice Hall, 3rd Edition, 2002.
2. M. Vidyasagar, Nonlinear systems analysis, 2nd Edition, Society of Industrial and Applied Mathematics, 2002.
References: (Format: Authors, Book Title in Italics font, Volume/Series, Edition Number,
1. H. Marquez,Nonlinear Control Systems, Analysis and Design, Wiley, 2003.
2. A. Isidori,Nonlinear Control Systems, Springer, 3rd Edition, 1995.
3. F. Verhulst,Nonlinear Differential Equations and Dynamical Systems, Springer, 2nd Edition, 1996.