Event-triggered SOF Control of Descriptor Switched Systems

In this paper, the co-design problem of static output-feedback (SOF) controller via event-triggered sampling (ETS) scheme for descriptor switched systems (DSSs) is investigated for the first time. Sufficient conditions are obtained using the average dwell-time approach and multiple Lyapunov functions to guarantee the closed-loop system is exponentially admissible (regular, impulse-free, and exponential stable). On the basis of these conditions, the controller gains and event-triggered conditions are are obtained by solving some strict linear matrix inequalities (LMIs). Finally, a numerical example is illustrated to verify the results and their efficiency.

I. Introduction

On the one hand, switched systems include a wide range of hybrid systems, and due to their multi-model mathematical description, the behavior of many physical and human-made systems can be decribed by them. Typically, a switched system consists of some subsystems and a switching signal law that is switched between them [1]. Switched systems have a variety of applications in industrial automation [2], chemical processes [3], network control systems [4], and flight control systems [5]. Furthermore, the descriptor model can provide a more general description of physical systems than the standard state-space model. Descriptor systems are also known as singular systems, differential-algebraic systems, degenerate systems [6–9]. In contrast to standard systems, algebraic equations exist in their mathematical model in addition to differential equations [7, 8]. Due to the presence of algebraic equations in the descriptor model, the analysis of descriptor systems is more complicated than the standard one. A descriptor system may not have the solution or may have impulsive behavior. Hence, regularity and impulse-freeness should be considered in addition to stability in descriptor systems [10, 11].