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Iterative Homogeneous Polynomial Lyapunov Functions Approach for Stabilizing Minimum Mode-Dependent Average Dwell Time Switched Systems via Output Feedback

A novel approach is proposed in this paper to design static output feedback controllers for asymptotically stabilizing continuous-time switched linear systems with minimum mode-dependent average dwell time (MMDADT). This approach adopts an iterative algorithm containing the solution of a traversal algorithm function and three optimization functions, the decision variables of which are established by the sum of squares (SOS) of matrix polynomials. The traversal algorithm function takes advantage of a polynomially parameter-bounded condition, allowing us to get the lower-bound of the Homogeneous Polynomial Lyapunov Functions’ (HPLFs) derivative. The first optimization function is a non-convex optimization function, which expresses a sufficient condition for stability analysis and computing MMDADT. The second and third optimization functions are both convex optimization functions, which are used to calculate the polynomially mode-dependent output feedback controllers. Two numerical examples are presented in order to show the feasibility of the proposed results.