Finite-time stability of linear systems: an approach based on polyhedral Lyapunov functions

Abstract

In this study, the authors consider the finite-time stability (FTS) problem for linear systems. Differently from previous studies, the authors assume that the sets to which the state variables must belong in order to satisfy the FTS requirement are boxes (or more in general polytopes) rather than ellipsoids. To deal with these more realistic constraints on the state variables the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than with the classical quadratic Lyapunov functions. The main result, derived by using polyhedral Lyapunov functions, is a sufficient condition for FTS of linear systems. Detailed analysis and design examples are presented to illustrate the advantages of the proposed methodology over existing methods.