Nonlinear Control Theory for Automation

The purpose of this chapter is to review some notions of fundamental importance on the analysis and design of feedback laws for nonlinear control systems. The first part of the chapter begins by reviewing the notion of dynamical system and continues with a discussion of the concepts of stability and asymptotic stability of an equilibrium, with emphasis on the method of Lyapunov. Then, it continues by reviewing the notion of input-to-state stability and discussing its role in the analysis of interconnections of systems. Then, the first part is concluded by the analysis of the asymptotic behavior in the presence of persistent inputs. The second part of the chapter is devoted to the presentation of systematic methods for stabilization of relevant classes of nonlinear systems, namely, those possessing a globally defined normal form. Methods for the design of full-state feedback and, also, observer-based dynamic output feedback are presented. A nonlinear separation principle, based on the use of a high-gain observer, is discussed. A special role, in this context, is played by the methods based on feedback linearization, of which a robust version, based on the use of extended high-gain observer, is also presented.