Robust Control Design for Linear Uncertain State Space Systems

Abstract

In this chapter, we focus our attention on the issues of robust stabilization and control design of linear uncertain systems with real parameter variations in state space framework. Recall that in the previous two chapters, we addressed the stability robustness and performance robustness from analysis viewpoint, whereas in this chapter, we address the aspect of controller synthesis for linear uncertain systems. Henceforth, we use the words synthesis and design interchangeably in the context of robust control. Towards this direction, this chapter presents various robust control design methodologies under three categories: (i) design via perturbation bound analysis; (ii) stabilization and performance issues via quadratic stability concept, which in turn include techniques labeled as “Riccati equation-based methods” as well as “guaranteed cost control” (GCC) methods; and finally (iii) design via robust eigenstructure assignment. These results are presented in the above mentioned order. In an attempt to consolidate these various methodologies in an overview perspective, only the salient features of the design procedures are discussed with the finer detailed design algorithms left to the original references in which they appeared. In line with the main focus of this book, design procedures dealing with only linear systems with linear controllers for systems described by linear state space models are considered. Also, only uncertain systems with linear time-varying and/or time-invariant real parameters belonging to a compact set are emphasized.