Sampled-data Based Dissipativity Control of T-S Fuzzy Markovian Jump Systems under Actuator Saturation with Incomplete T
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Sampled-data Based Dissipativity Control of T-S Fuzzy Markovian Jump Systems under Actuator Saturation with Incomplete Transition Rates Tianshu Xu, Jianwei Xia*, Xiaona Song, Zhen Wang, and Huasheng Zhang Abstract: In this paper, the topic of sampled-data based dissipativity control for Takagi-Sugeno (T-S) fuzzy Markovian jump systems with incomplete transition rates and actuator saturation is addressed. First of all, by constructing an appropriate two-sided closed-loop function that captures the realistic information of sampling pattern, together with the free-matrix-based inequality approach, a sufficient condition is developed to ensure the considered systems to be strictly(Q,S,R)-γ-dissipative. Then, the corresponding mode-dependent sampled-data controllers are designed based on the given dissipativity condition. As a corollary, the controller design is presented for the system without disturbance. Furthermore, an optimization problem is investigated in order to maximize the domain of the attraction. Finally, simulation examples are offered to verify the feasibility of the results. Keywords: Actuator saturation, dissipative control, fuzzy Markovian jump systems, incomplete transition rates, sampled-data control.
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INTRODUCTION
In recent years, a growing number of scholars have developed a strong interest in fuzzy control of nonlinear systems, and there have plenty of successful applications. In particular, the Takagi-Sugeno (T-S) fuzzy model [1], which can provide a powerful way to connect linear system theory with fuzzy logic theory, plays an important role in various control technologies [2–14]. This fuzzy model is described by a set of IF-THEN rules, which essentially combines simple subsystems together to obtain the overall system fuzzy model. Generally speaking, most of the subsystem models are linear, meaning that complex nonlinear systems can be managed by the results of linear systems. For example, a survey of recent advances on fuzzy-model-based nonlinear networked control systems was proposed in [3]. The authors in [4] have studied optimal guaranteed cost sliding-mode control for a class of interval type-2 fuzzy time-delay systems. The issue of robust L1 observer-based Non-PDC controller design for persistent bounded disturbed T-S fuzzy systems was discussed in [6]. Adaptive fuzzy control for several nonlinear systems with full state constraints or unknown control directions were deeply discussed in [8–14]. Recently, based on this fuzzy model, researchers began to turn their
attention to the research of fuzzy markovian jump systems(FMJSs). For instance, the topics of sliding mode control, non-fragile H∞ control for FMJSs were discussed in [15] and [16], respectively. For the case of FMJSs with partially known transition probabilities, the problems of H∞ control and composite anti-disturbance resilient control were studied in the literature [17, 18]. In another area of research, random changes are often occurring in dynamical systems, w
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