An extension of the KYP-lemma for the design of state-dependent switching systems with uncertainty

We consider the problem of designing state-dependent linear switching systems subject to parameter uncertainty. The switching rule is governed by a fixed partition of the state-space, and the parameter uncertainty appears in the matrices which determine the resulting dynamics. We derive a KYP-like lemma that can be used to design such systems in a manner that guarantees quadratic stability, for an arbitrary number of independent switching rules, each with its own switching region and its own domain of parameter uncertainty. Examples are given to illustrate the usefulness of our result.