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

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Chapter Six

Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions

6.1 Introduction

The notions of asymptotic and exponential stability in dynamical systems theory imply convergence of the system trajectories to an equilibrium state over the infinite horizon. In many applications, however, it is desirable that a dynamical system possesses the property that trajectories that converge to a Lyapunov stable equilibrium state must do so in finite time rather than merely asymptotically. Most of the existing control techniques in the literature ensure that the closed-loop system dynamics of a controlled system are Lipschitz continuous, which implies uniqueness of system solutions in forward and backward times. Hence, ...

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