Chapter 1 - Observer-Based Controller of Analytical Complex Systems: Application for a Large-Scale Power System

Abstract

This chapter is devoted to nonlinear control with the state observer of complex systems modeled in polynomial form. This kind of system presents the advantage of having the capacity of representing an important class of nonlinear systems and describing accurately the dynamic behavior of many physical processes. The basic idea is to design a nonlinear control law with a state observer, guaranteeing the overall asymptotic stability of the augmented system formed by the nonlinear process, the control, and the observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state-space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method.