A stability criterion for asynchronously switched linear systems via sampled-data control

Abstract

This paper considers an asynchronous problem for sampled-data control of switched linear systems, which are described as switched linear systems with an input delay. To handle the problem, this paper proposes a stability criterion for the systems by constructing a novel Lyapunov-Krasovskii functional dependent not on system modes but on controller modes. The functional continuously remains when the system modes are switched but discontinuously changes whenever the controller mode moves to the current system mode at the sampling instants. Furthermore, the functional is allowed to increase or decrease up to a certain level when the functional discontinuously changes and to increase up to a certain level when the system modes and the controller modes are asynchronous. Based on the functional, this paper derives an average dwell time associated with the interval of samplings and the incremental level of the functional for guaranteeing the stability of the systems. A numerical example illustrates the validation of the proposed method.