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

Abstract

In this paper we consider the finite-time stability problem for linear systems. Differently from previous papers, the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than with the classical quadratic Lyapunov functions. In this way we are able to manage more realistic constraints on the state variables; indeed, in a way which is naturally compatible with polyhedral functions, we assume that the sets to which the state variables must belong in order to satisfy the finite-time stability requirement are boxes (or more in general polytopes) rather than ellipsoids. The main result, derived by using polyhedral Lyapunov functions, is a sufficient condition for finite-time stability of linear systems, which can also be used in the controller design context. Detailed analysis and design examples are presented to illustrate the advantages of the proposed methodology over existing methods.