Uniform asymptotic stabilization of nonlinear switched systems with arbitrary switchings and with dynamic uncertainties by means of small gain theorems

The paper focuses on the problem of global uniform asymptotic stabilization of switched triangular form systems with unobservable dynamic uncertainties and with unknown switching signal. We prove that if the dynamic uncertainty is treated as external disturbance, then the triangular system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty. Then, using an extension of the well-known small gain theorem to the case of switched systems with arbitrary switchings, we obtain the uniform asymptotic stabilization of the overall interconnected system.