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

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Chapter Five

Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions

5.1 Introduction

One of the most basic issues in system theory is the stability of dynamical systems. The most complete contribution to the stability analysis of nonlinear dynamical systems is due to Lyapunov [128]. Lyapunov’s results, along with the Krasovskii-LaSalle invariance principle [116, 120, 121], provide a powerful framework for analyzing the stability of nonlinear dynamical systems. Lyapunov methods have also been used by control system designers to obtain stabilizing feedback controllers for nonlinear systems. In particular, for smooth feedback, Lyapunov-based methods were inspired by Jurdjevic and Quinn [105] who give sufficient conditions for ...

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