Delay-Dependent Robust Dissipative Filter for T-S Fuzzy Descriptor Time-Varying Delay Systems
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Delay-Dependent Robust Dissipative Filter for T-S Fuzzy Descriptor Time-Varying Delay Systems Yuechao Ma1 · Menghua Chen1
Received: 22 December 2014 / Revised: 5 May 2015 / Accepted: 9 June 2015 © Brazilian Society for Automatics–SBA 2015
Abstract This paper deals with the delay-dependent robust dissipative filter for a class of T-S fuzzy descriptor systems with parameter uncertainties. Based on Lyapunov stability theory, sufficient conditions on the existence of robust dissipative filters is derived, which guarantee that the filter error system is asymptotically stable with a dissipative index. And the design of a delay-dependent filter can be obtained by solving the linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness and superiority of the obtained results. Keywords T-S fuzzy model · Descriptor system · Time-varying delay · Robust dissipative filter
1 Introduction Signal often suffers from external or internal interference during the process of transmission and testing inevitably. In order to obtain the desired signal and eliminate interference, the method of filtering is generally being used, and it has come to play an important role in fuzzy model during the past years. Shi et al. (2012) discussed the problem of H∞ filtering for discrete-time systems with stochastic incomplete measurement. Descriptor systems are often used in the network, economy, robotics, and other fields, and they have attracted more and more concern of the scholars such as Diego et al. (2014). Since 1999, Tanguchi spread the normal T-S fuzzy model into a more generalized condition and put forward T-S fuzzy
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Menghua Chen [email protected] School of Science, Yanshan University, 438 Hebeidajie Road, Qianhuangdao, Hebei, People’s Republic of China
descriptor system model in Taniguchi et al. (1999), which has developed a new way for the investigation of nonlinear descriptor system and time-varying system. Afterward, on the base of this model, there have been significant results in the study of T-S fuzzy time-delay descriptor systems, see Ma and Yan (2013), Yuan et al. (2009) and Bouarar et al. (2010). Li et al. (2014) investigated the problem of fuzzy model-based D-stability and non-fragile control for discretetime descriptor systems with multiple delays. Over the past few years, the filtering of descriptor system is especially important and has been extensively studied, such as Xu and Lam (2007), Wu et al. (2010), and Lu et al. (2007). Lu et al. (2010) proposed H∞ filtering design for singular systems with communication delays. For discrete-time singular systems, Kim (2010) discussed the robust H∞ filtering. In addition, since 1970s, the dissipative system theory has played an important role in the system-stability process. The passivity control for a kind of T-S fuzzy descriptor system has been studied in Zhu et al. (2006). Recently, the robust dissipative filter has attracted much interest in academics, and the dissipative filter for discrete fuzzy systems is presented in Lo and Wu
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