Stochastic Switched Sampled-Data Control for Uncertain Fuzzy Systems with Packet Dropout
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Stochastic Switched Sampled-Data Control for Uncertain Fuzzy Systems with Packet Dropout Chao Ge1 • Liu Yang1 • Zhiwei Zhao2 • Jiayong Zhang3 • Yajuan Liu4
Received: 2 May 2020 / Revised: 14 July 2020 / Accepted: 18 October 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract This paper addresses the stability and stabilization problems of uncertain Takagi–Sugeno (T-S) fuzzy system with control packet dropout. The process of packet loss is proposed, which is modeled according to some white noise sequences of Bernoulli distribution. Then, under the zero-input strategy, a newly stochastic switched sampled-data controller is introduced. Based on the Lyapunov function method, a novel Lyapunov–Krasovskii (LKF) function is constructed via introducing a fuzzy membership functions (FMFs), which can use the information about the actual sampling pattern. Each term of the LKF need not be positive, but it needs to be positive at sampling instants. Using the reciprocally convex method and relaxed free-matrix-based (FMB) integral inequality, novel stabilization criteria are established to guarantee that the T-S fuzzy system is stochastic stable when the control packet dropout occurs in a random way. Based on the linear matrix inequalities (LMIs), a fuzzy controller design algorithm for sampled data is presented to obtain a larger sampling interval. Finally, two numerical examples are
& Chao Ge [email protected] & Jiayong Zhang [email protected] 1
Institute of Electrical Engineering, North China University of Science and Technology, Tangshan 063009, China
2
Department of Computer Engineering, Tangshan College, Tangshan 063009, China
3
Institute of Mining Engineering, North China University of Science and Technology, Tangshan 063009, China
4
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
used to verify the effectiveness and advantages of the proposed method. Keywords Sampled-data control T-S fuzzy system Stochastic switched system Packet dropout
1 Introduction The T-S fuzzy model [1] has been widely used in the analysis and synthesis for nonlinearity systems, which can approach the nonlinear system with arbitrary precision in the set of convex compact [2–4]. In recent years, the stability analysis of T-S fuzzy system and controller synthesis have been deeply investigated and also gained a lot of results [5–8]. On the other hand, an inevitable disadvantage that we should not ignore is the parameter uncertainties for T-S fuzzy systems due to the model inaccuracies, unexpected exterior perturbations and network-generated stochastic failures in the implementation of the system [9–12]. For example in [13], the authors investigated the H1 controller design problem for uncertain T-S fuzzy system via the parallel distributed compensation (PDC). By introducing some free weighting matrices to deal with the integral items and converting the coupling time-varying matrix inequalities into a group of decoupling matrix inequalities, some novel criteria for uncertain fuzzy
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