Generalized fault detection for two-dimensional Markovian jump systems

Wu, Ligang; Yao, Xiuming; Zheng, Wei Xing

doi:10.1016/j.automatica.2012.05.024

Cited by 210 publications

(79 citation statements)

References 27 publications

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“…Proof : Based on some straightforward algebraic manipulations and under the initial conditions (26), we can see that the inequalities (23) and (24) imply (20), and the inequality (25) is equivalent to (21). Therefore, according to Theorem 1, Theorem 2 and Corollary 1, the H ∞ index defined in (16) satisfies J 1 < 0 and, at the same time, the system state covariances achieves…”

Section: Theorem 3 Consider the Discrete Time-varying Nonlinear Stochmentioning

confidence: 97%

“…A large body of literature has been devoted to the stochastic control or filtering problem for different systems such as polynomial stochastic systems [1,2,4], Markovian jumping systems [20], switched stochastic systems [13], discrete-time stochastic systems with state-dependent noises [17], nonlinear stochastic systems [8,19] and stochastic sampled-data control system [21]. Among various stochastic control schemes, the covariance control (CC) theory has gained particular research attention due primarily to the fact that the performance requirements of many engineering control systems are naturally expressed as the upper bounds on the steady-state variances [11].…”

Section: Introductionmentioning

confidence: 99%

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Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

et al. 2016

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In this paper, a general event-triggered framework is set up to deal with the variance-constrained H∞ control problem for a class of discrete time-varying systems with randomly occurring saturations, stochastic nonlinearities and state-multiplicative noises. Based on the relative error with respect to the measurement signal, an event indicator variable is introduced and the corresponding event-triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not. The stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well-studied nonlinearities. A set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations, stochastic nonlinearities and state-dependent noises. The purpose of the addressed multiobjective control problem is to design a set of time-varying output feedback controller such that, over a finite horizon, the closed-loop system achieves both the prescribed H∞ noise attenuation level and the state covariance constraints. A recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite-horizon controllers, and the analytical characterization of such controllers is also given. Simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme.

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Section: Theorem 3 Consider the Discrete Time-varying Nonlinear Stochmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

et al. 2016

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“…In the case of packet loss and time delay, at home and abroad, the scholars are researching the problem about the performance analysis of the network control system with ∞ output tracking and the design issues of controller [34]. In literatures [35,36], the faulty links of communication are often described by the Markov chain and the distribution of Bernoulli random variables. In literature [37], under the links of imperfect communication, the feedback control of ∞ output has been studied for the systems of the same category.…”

Section: Introductionmentioning

confidence: 99%

H∞ Tracking Control of Fuzzy Dynamic Output for Nonlinear Networked System with Packet Dropouts

Wang

2018

Mathematical Problems in Engineering

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The tracking control of ∞ dynamic output feedback is proposed for the fuzzy networked systems of the same category, in which each system is discrete-time nonlinear and is missing measurable data. In other words, the loss of data packet occurs randomly in both the uplink and the downlink. The independent variables that are called the Bernoulli random variables are considered to design the loss of data packets. The method of parallel distributed compensation (PDC) in terms of the T-S fuzzy model is applied to investigate the dynamic controller of tracking control on the systems. Then, it is presented that the analytical ∞ performance of the output error between the reference model and the fuzzy model for the closed-loop system containing dynamic output feedback controller is proven. Furthermore, the achieved sufficient conditions in terms of LMIs ensure that the closed-loop system is stochastically stable in the ∞ sense. Finally, a numerical system is offered to show the effectiveness of the established technique.

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“…Recently, a lot of research has been done in fault diagnosis for both linear and nonlinear systems in the presence of event-triggered scheme, Markovian jump phenomena, and unknown membership functions etc. For example, in [3], the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme was investigated, in [4], H 2 fault-detection observer for two-dimensional (2-D) discrete-time Markovian jump systems was proposed, and in [5], a simultaneous fault-detection and control strategy was proposed for switched linear systems with mode-dependent average dwell-time. In [6,7], fuzzy fault-detection observers were designed, particularly, a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to reduce conservatism in [6], and an integrated observer-based fault-detection scheme was proposed to meet the real-time fault-detection requirements from industrial processes in [7].…”

Section: Introductionmentioning

confidence: 99%

Adaptive fault estimation for T-S fuzzy systems with unmeasurable premise variables

Liu

Wang

et al. 2018

Adv Differ Equ

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This paper is concerned with the fault estimation problem for a class of Takagi-Sugeno (T-S) fuzzy systems with actuator faults and sensor disturbances. Premise variables of the T-S fuzzy systems are assumed to be unmeasurable such that conventional parallel distributed compensation (PDC) methods are not applicable. A modified adaptive observer is designed to estimate states and fault parameters simultaneously. Finally, a simulation example is presented which shows the effectiveness of the proposed method.

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Generalized fault detection for two-dimensional Markovian jump systems

Cited by 210 publications

References 27 publications

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

H∞ Tracking Control of Fuzzy Dynamic Output for Nonlinear Networked System with Packet Dropouts

Adaptive fault estimation for T-S fuzzy systems with unmeasurable premise variables

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