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Stability and Control of Large-Scale Dynamical Systems by Sergey G. Nersesov, Wassim M. Haddad

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Chapter Two

Stability Theory via Vector Lyapunov Functions

2.1 Introduction

In this chapter, we introduce the notion of vector Lyapunov functions for stability analysis of nonlinear dynamical systems. The use of vector Lyapunov functions in dynamical system theory offers a flexible framework for stability analysis because each component of the vector Lyapunov function can satisfy less rigid requirements as compared to a single scalar Lyapunov function. Specifically, since for many nonlinear dynamical systems constructing a system Lyapunov function can be a difficult task, weakening the hypothesis on the Lyapunov function enlarges the class of Lyapunov functions that can be used for analyzing system stability. Moreover, in the analysis of large-scale ...

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