Multiobjective Fault-Tolerant Control for Fuzzy Switched Systems With Persistent Dwell Time and Its Application in Electric Circuits

IEEE Trans. Fuzzy Syst.

Xia

Shen

et al. 2021

Self Cite

254

105

This paper investigates the non-fragile H∞ synchronization issue for a class of discrete-time T-S fuzzy Markov jump systems. With regard to the T-S fuzzy model, a novel processing method based on matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of actuator, a non-fragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this paper lies in that the transition probabilities of Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed H∞ performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results. Index Terms-T-S fuzzy Markov jump chaotic systems, persistent dwell-time switching, mean-square exponential stability, non-fragile H∞ synchronization.

Section: Introductionmentioning

confidence: 99%

$\mathcal {H}_{\infty }$ Synchronization for Fuzzy Markov Jump Chaotic Systems With Piecewise-Constant Transition Probabilities Subject to PDT Switching Rule

IEEE Trans. Fuzzy Syst.

Xia

Shen

et al. 2021

Self Cite

254

105

“…Finally, the effectiveness of the designed controller is verified by a numerical example. The notations used are standard and one can refer to [42] for more details. In addition, other important notations about the PDT switching rule are highlighted below.…”

Section: ) By Fully Considering the Features Of Nsspss Propermentioning

confidence: 99%

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

Liu

Xia

et al. 2022

IEEE Trans. Cybern.

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This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H ∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example. Index Terms-Interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, persistent dwell-time (PDT) switching rule, quantized control, singularly perturbed nonlinear systems. I. INTRODUCTION S OME parasitic parameters, such as small time constants, capacitances, and inductances, may increase the order of dynamic equations and lead to the numerical ill-conditioning problem. In order to overcome these obstacles, the singular perturbation technique is usually employed. Examples of singularly perturbed systems (SPSs) are power systems, airplanes, and so on [1]-[3]. When discretizing continuous-time SPSs, the sampling period influences the discrete-time model, which

“…The authors in [29] analyzed the problem of asymptotic gain and adaptive control for PDTSR-based switching systems. In [30], the problem of designing the output feedback controller for switching systems based on PDTSR was analyzed. Although PDTSR has advantages, little literature has introduced it into the research of discrete-time GRNs due to its complexity.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time H State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties

IEEE/ACM Trans. Comput. Biol. and Bioinf.

Shen

et al. 2022

Self Cite

This paper is concerned with the problem of finitetime H∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this paper is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method. Index Terms-Switched genetic regulatory networks, finitetime H∞ state estimation, persistent dwell-time switching rule, randomly occurring uncertainties.