An LMI-based algorithm for switching state-feedback control of continuous-time switched systems

This paper proposes an algorithm based on LMIs to simultaneously design a switching control law and state-feedback gains that robustly stabilize a continuous-time switched linear system. The method is based on the computation of a stable convex combination of a polytope of matrices. First, the problem is reformulated as a relaxed LMI condition where the scalar parameters appear affinely. Differently from the majority of existing approaches, that resort to the use of gridding, a stable convex combination is determined through an iterative procedure. The algorithm is then extended to provide at the same time a switching strategy and the gains that stabilize the closed-loop system, also including the maximization of a bound to the decay rate. Numerical examples illustrate the results.