On Reliable Stabilization via Rectangular Dilated LMIs and Dissipativity-Based Certifications

In this short note, we consider the problem of reliable stabilization for multi-channel systems, where our main objective is to maintain the robust stability of the perturbed closed-loop system when there is a single controller failure in any of the control channels. Specifically, we present a less-conservative result than results in the literature in terms of a set of dilated LMIs for the reliable state-feedback stabilization of the nominal system, while a dissipativity-based certification is used to extend the stability condition when there is an additive model perturbation in the system. Finally, a numerical example is presented to illustrate the applicability of the proposed technique.