Syllabus

Introduction: Nonlinear system behavior, Nonlinear control.

Nonlinear system analysis: Phase plane analysis: Concepts of phase plane analysis, phase plane analysis of linear and nonlinear systems, Existence of limit cycles, Fundamentals of Lyapunov 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, Per- formance analysis. Control design based on Lyapunov’s direct method.

Advanced stability theory: Concepts of stability for Non-autonomous systems, Lyapunov anal- ysis of non-autonomous systems, instability theorems, Existence of Lyapunov functions, Barba- lat’s Lemma and stability analysis, Positive real systems: PR and SPR Transfer functions, The Kalman-Yakubovich Lemma.

The passivity Formalism: passivity in linear systems., Absolute stability, Establishing bound- edness of signals, Existence and Unicity of solutions. Nonlinear Control systems design: Feedback Linearization and the canonical form, Input-state Linearization of SISO systems, Input-output Linearization of SISO systems, multi input systems.

Sliding Control: Sliding surfaces, Filippov’s construction of the equivalent dynamics, direct implementations of switching control laws, Continuous approximations of switching control laws, modeling and performance trade-offs Lie derivative, Lie Bracket, Back stepping method for non-feedback linearizable systems.