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Virtually all physical systems are nonlinear in nature. Sometimes, it is possible to describe the operation of a physical system by a linear model, e.g., as a set of ordinary linear differential equations. This is the case, for example, if the mode of operation of the physical system does not deviate too much form the nominal set of operating conditions, i.e., one can linearize the system. Thus, the analysis of linear systems occupies an important place in system theory. But in analyzing the behavior of a physical system, one often encounters situations where the linear (or linearized) model is inadequate or inaccurate; that is the time when concepts of this course may prove useful.

The goal of the course is to address several main subjects in nonlinear control theory. We extend the notion of Lyapunov stability to systems with input i.e., input-to-state stability, show how Lyapunov stability is related to input-output stability and present/apply various nonlinear control design tools; integral control, Lyapunov redesign, control Lyapunov function.