Robust commutation time for switching polynomial systems

This paper considers the stability analysis of switching polynomial systems. In particular, the problem of computing upper bounds of the minimum commutation time ensuring stability with respect to finite and infinite input sequences is dealt with. It is shown that such upper bounds can be established by solving LMI feasibility tests for given polynomial Lyapunov functions in the former case and homogeneous polynomial Lyapunov functions in the latter case. Lastly, the structure of the obtained tests is exploited to derive a search for less conservative upper bounds in a reduced number of variables through the solution of convex LMI optimizations at each iteration.