The small-gain theorem for linear systems and its applications to robust stability

Abstract

In a system consisting of the interconnection of several component subsystems, some of which could be only poorly modeled, stability analysis and feedback design might not be easy tasks. Thus, methods allowing to understand the influence of interconnections on stability and asymptotic behavior are important. The methods in question are based on the use of a concept of gain, which can take alternative forms and can be evaluated by means of a number of alternative methods. This chapter describes the various alternative forms of such concept of gain, and shows why this is useful in the analysis of stability of interconnected systems. A major consequence is the development of a systematic method for stabilization in the presence of (general class of) model uncertainties.