Robust/reliable stabilization of multi-channel systems via dilated LMIs and dissipativity-based certifications

In this paper, we consider the problem of reliable stabilization for a multi-channel system, where our main objective is to maintain the stability of the perturbed closed-loop system and when there is a single controller failure in any of the control channels. We specifically present a computationally tractable and less-conservative result 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 under model perturbation in the system. Finally, a numerical example is used to demonstrate the applicability of the proposed technique.