Event-triggered Control for Switched Affine Linear Systems
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Event-triggered Control for Switched Affine Linear Systems Hongsheng Hu, Shipei Huang*, and Zhengjiang Zhang Abstract: Event-triggered control problem for switched affine linear systems with a state-dependent switching law is addressed in this paper. By constructing a piecewise differential Lyapunov function with time-scheduled matrices, an event-triggered scheme and a switching signal are proposed. The switching signal depends on the state of the trigger instant. A sufficient condition is developed to ensure that the switched affine system exponentially convergences to a small neighborhood of the desired equilibrium point. The proposed result is then generated to a disturbance attenuation performance analysis. The results are presented in the form of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed results. Keywords: Affine systems, disturbance attenuation performance, event-triggered control, switched systems.
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INTRODUCTION
A switched system is a hybrid system which has received the attention of scholars due to their applications in many areas, such as physical systems, chemical processes, aircraft control, networked control systems, and so on [1]. Such system consists of a number of subsystems and a logical law between them. The stability analysis and controller design of switched systems are important issues and have been studied by many scholars in the past few decades [2–6]. For example, the literature [2] studied the stability analysis of switched linear systems under switching conditions, and gave the necessary and sufficient conditions for asymptotic stability. A hidden Markov model-based nonfragile state estimator was designed for switched neural network with probabilistic quantized outputs in [3]. A multi-step and multi-class Lyapunov functions method was proposed to investigate the asymptotic stability of discrete-time switched systems with time-varying switching signals in [4]. Static output feedback control of switched systems with quantization was investigated by utilizing a nonhomogeneous sojourn probability approach in [5]. Considering that there exist various disturbances in practical engineering, H∞ performance or L2 -gain performance analysis and control were also investigated, and many important results were developed in the literature. For instance, combining the multiple Lyapunov function method with the average dwell time approach, sufficient conditions for asymptotically stabil-
ity with L2 -gain performance were obtained in [6]. By constructing a proper Lyapunov function, sufficient conditions for the existence of nonstationary L2 -L∞ filter for Markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities was proposed in [7]. As a special class of switched systems, switched affine systems have also received extensive attention. Many practical systems can be described as switched affine systems, such as converters in power elec
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