Aperiodic sampled‐data stabilization of switched singular systems with asynchronous switching: A hybrid control approach

Abstract

This article investigates the sampled‐data stabilization problem for a class of switched singular systems with aperiodic sampling. The asynchronous switching between the plant and the switched controller caused by sampling is considered. Unlike normal systems, the conventional zero‐order hold type sampled‐data control law may be inapplicable to singular systems. This is because under that control law, the algebraic equations of singular systems may have no solutions at sampling instants. To cope with this problem, a new hybrid control law composed of a mode‐dependent impulsive controller and a mode‐dependent sampled‐data state feedback controller is devised. The impulsive controller adjusts the values of differential substate at sampling instants so that the algebraic equations are solvable. Then, by constructing a novel piecewise sampling‐time‐dependent Lyapunov function and using the average dwell time method as well as convex technique, a sampling‐range‐dependent sufficient condition for exponential stability of the resulting closed‐loop system is established. Moreover, an optimization‐based method is proposed to solve the hybrid controller gains. Simulation results on two examples including a mechanical arm system show the effectiveness of the proposed control method.