Finite-Time Asynchronously Switched Control of Switched Systems with Sampled-Data Feedback

Modern control systems usually employ digital technology for controller implementation. The dynamics of the systems are naturally continuous, while control inputs are usually discrete when digital control is utilized. This paper deals with the finite-time stabilization problem of switched systems with sampled-data state feedback under asynchronous switching. The asynchronous switching idea originates from the fact that switching instants of the controllers lag behind or exceed those of subsystems. The attention is focused on designing an asynchronously switched sampled-data controller that guarantees the finite-time stability of the dynamic system. Especially, we consider the case that the switching time and sampling time are not uniform when the system is working. On the basis of finite-time stability theory and multiply Lyapunov functions approach, a finite-time stability condition related to dwell time and sampling period is established. Then, an asynchronously switched sampled-data controller is designed, and the corresponding switching law is also derived to guarantee the considered system to be finite-time stable. Two numerical examples are provided to show the effectiveness of the developed results.