Cyclic switching laws for practical stability of integrator switched systems with constant period time

Abstract

We study the practical stability of the integrator switched systems with the constant period time under the cyclic switching laws, of which the switching sequence is cyclic and each cycle's period time is constant. Our aim is to establish significant switching laws which allow us to obtain the individual switching duration sequence for each cycle such that the integrator switched system is practically stable. We develop a new decomposition expression of the switching duration sequences, and show that a switching duration sequence can be divided into two parts: one part contributes to the change of state during the cycle and another one is about the nonnegativity of the duration sequence. Based on the decomposition expression, a sufficient condition for the existence of the switching duration sequences are induced. We propose a switching law which ensures the practical stability of the nominal integrator switched systems with the constant period time. Also, we propose another switching law which ensures the practical stability of the uncertain integrator switched systems and provide an upper bound of the uncertainties. The applicability of two proposed switching laws is illustrated by numerical simulations.