Static Output Feedback Control of Switched Systems with Dwell Time Constraints or Arbitrary Switching

This paper addresses the problem of determining static output feedback controllers for stabilizing continuous-time switched linear systems with either dwell time constraints or arbitrary switching. This problem is addressed by searching for a family of homogeneous polynomial Lyapunov functions (HPLFs) parameterized by the sought controller that prove stability for the considered set of switching rules. In order to conduct this search, polynomials are introduced for approximating the matrix exponential and for quantifying the feasibility of the Lyapunov inequalities. It is shown that there exists a stabilizing controller if and only if a condition built solving three convex optimization problems with linear matrix inequalities (LMIs) holds for polynomials of degree sufficiently large.