Abstract
The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.
Highlights
T-S fuzzy systems have gained a lot of attentions in the recent years mostly due to fuzzy systems being the omnipotent simulator of nonlinear systems [1]
Based on the common Lyapunov function (CLF), the stability conditions of such systems are proposed via linear matrix inequalities (LMIs) in [5]. en, considering the conservatism of the CLF in the stability analysis, a fuzzy Lyapunov function is given in [6] to study this kind of systems
Afterwards, considering the system with time delay, the parallel distribution compensation (PDC) controller design method of these systems is given without all the subsystems which are regular and impulse-free in [10]
Summary
T-S fuzzy systems have gained a lot of attentions in the recent years mostly due to fuzzy systems being the omnipotent simulator of nonlinear systems [1]. Based on the above analysis, in this paper, the finite-time admissibility issues of T-S fuzzy singular stochastic systems with distinct differential term matrices and Brownian parameter perturbations are discussed via FLF. The innovative sufficient condition is proposed to ensure that these systems are finite-time admissible via strict LMIs. en, a novel design approach of fuzzy PDC controller is given, which avoids solving bilinear matrix inequalities. (i) e finite-time admissibility analysis and controller design for T-S fuzzy singular stochastic systems with distinct differential term matrices and Brownian parameter perturbations are studied. This kind of systems can describe a wide range of nonlinear singular stochastic systems, and many actual systems are described more and naturally by such systems. The controller design becomes simple and effective in form of strict LMIs
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