On the peak of the response of structured polytopic linear systems

This paper addresses the problem of determining the peak of the response of a linear system whose system matrices are polynomial functions of a time-invariant uncertainty vector constrained into a polytope. A novel approach is proposed for obtaining upper bounds of the sought peak based on the construction of a structured polynomial Lyapunov function in the state and in the uncertainty. In particular, a sufficient condition is provided for establishing whether a chosen quantity is an upper bound of the sought peak in terms of feasibility of a system of linear matrix inequalities (LMIs). The proposed approach is illustrated by some numerical examples.