Sandwich control systems with impulse time windows
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ORIGINAL ARTICLE
Sandwich control systems with impulse time windows Yuming Feng1,2 • Chuandong Li1 • Tingwen Huang3
Received: 13 January 2016 / Accepted: 6 August 2016 Ó Springer-Verlag Berlin Heidelberg 2016
Abstract In this paper, we formulate a new system, named by sandwich control system with impulse time windows. The present system is a cyclic control system, composed of three parts in a round: the first and last parts are continuous subsystems, while the middle one includes an impulsive operation. Different from the most existing results for impulsive systems, we assume that the impulse moments are unknown but limited to certain intervals (namely, impulse time windows). We then study the stability of the considered systems and obtain an exponential stability criterion in terms of a set of linear matrix inequalities. As a numerical example, Chua oscillator is stabilized by the proposed method. Keywords Sandwich control system Impulse time windows Lyapunov function Exponential stabilization Chua’s oscillator
& Chuandong Li [email protected] Yuming Feng [email protected] Tingwen Huang [email protected] 1
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic Information Engineering, Southwest University, Chongqing 400715, People’s Republic of China
2
Key Laboratory of Nonlinear Science and System Structure, School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404100, People’s Republic of China
3
Department of Mathematics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
1 Introduction Many methods are used to stabilize the nonlinear system, for example, adaptive fuzzy controls are employed in systems in [1, 2]. Yin et al. have studied adaptive fuzzy control of strict-feedback nonlinear time-delay systems with unmodeled dynamics in [1] and fuzzy adaptive tracking control methods are used to nonlinear switched stochastic pure-feedback systems in [2]. In [4] Data-Driven control is applied. Other interesting works in this aspect are listed in [3–10]. Impulsive control methods can be found, for example, in [11–14]. Impulsive control can provide an efficient method for some cases in which the systems cannot endure continuous disturbance. For impulsive control systems with impulse time windows we mean that for the systems the impulses may occur in an unexpected time but are limited to time windows. Figure 1 shows the distribution of impulse moments and impulse time windows. Switch control method is a kind of discontinuous control method and has a lot of applications, e.g., [15–21]. Within one period of a such system, there are more than one continuous inputs, i.e., the switch control system contains many continuous subsystems. We attempt to combine the switch control method with impulsive control one together. First we choose a switch system which contains three continuous subsystems, for first and last subsystems, continuous inputs are imposed. And for the middle subsystem, an impulse
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