Convex relaxations for L₂-gain analysis of piecewise affine/polynomial systems

Abstract

This paper proposes some sufficient conditions based on the computation of polynomial and piecewise polynomial storage functions for -gain analysis of discrete-time piecewise affine or piecewise polynomial systems. The computation of such storage functions is performed by means of convex optimisation techniques via the sum-of-squares decomposition of multivariate polynomials.

Keywords:

• piecewise affine and piecewise polynomial discrete-time systems
• -gain
• storage functions
• convex optimisation
• sum-of-squares decomposition