<i>H<sub>∞</sub>
                  </i> Filtering for Nonhomogeneous Markovian Jump Repeated Scalar Nonlinear Systems With Multiplicative Noises and Partially Mode-Dependent Characterization

Hua, Mingang; Zheng, Dandan; Deng, Feiqi; Fei, Juntao; Cheng, Pei; Dai, Xisheng

doi:10.1109/tsmc.2019.2919146

Cited by 40 publications

(13 citation statements)

References 53 publications

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“…5 The semi-Markovian switched systems are a class of randomly switched systems, in which the switching signal is modeled by a semi-Markovian process. 6,7 Comparing with Markovian switched systems, [8][9][10][11][12] semi-Markovian switched systems can remove the restriction of sojourn times obeying exponential distribution. For a semi-Markovian switched system, sojourn times of each subsystems can be non-exponentially distributed, and transition rates are time-varying.…”

Section: Introductionmentioning

confidence: 99%

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

2021

Math Methods in App Sciences

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This paper investigated the almost surely exponential stability (ES a.s.) for semi-Markovian switched singular stochastic systems (SSSSs) with mode-dependent ranks, in which the derivative matrices E i have different ranks. Due to the constraint of consistent initial conditions, state jumps may occur at switching instants in switched singular systems. Some more general conditions for the existence and uniqueness of the solution of semi-Markovian SSSSs with mode-dependent ranks are given together with a detailed analysis of state jumps. Based on the equivalent systems transformation and multiple Lyapunov functions method, novel conditions of ES a.s. are presented for addressed systems. An example is given to explain the effectiveness of developed results.

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Section: Introductionmentioning

confidence: 99%

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

2021

Math Methods in App Sciences

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“…References and studied the problems of H ∞ control and output feedback control for nonhomogeneous MJSs, respectively. The problem of filtering for nonhomogeneous MJSs via H ∞ , l 2 − l ∞ , or fuzzy approach was investigated. Recently, the observer‐based H ∞ control for nonhomogeneous MJSs with nonlinear input was proposed in Reference .…”

Section: Introductionmentioning

confidence: 99%

Robust finite‐time H_∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

Xing

Gao

et al. 2020

Intl J Robust & Nonlinear

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In this article, the problem of robust finite-time H ∞ synchronization control is investigated for a class of uncertain discrete-time master-slave systems with Markovian switching parameters in the observer-based case. Parameter uncertainties are assumed to be norm-bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain.By using stochastic Lyapunov function method and finite-time analysis techniques, novel sufficient conditions that include the master-slave parameters are obtained for designing an observer-based finite-time H ∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations. K E Y W O R D Sfinite-time control, nonhomogeneous Markovian jump systems, observer-based control, parameter uncertainties, synchronization INTRODUCTIONMarkovian jump systems (MJSs), as a class of stochastic hybrid systems, have received a great deal of interest due to their effectiveness of modeling dynamic systems with random abrupt changes on structures and parameters. What characters these systems is that the system modes evolve subject to a Markov chain, which follows its own transition probabilities (TPs). Much attention has been devoted to the research to obtain more appropriate assumptions on TPs, 1-5 for the reason that traditionally ideal assumption on TPs limits the applicability of the relevant results. Significantly, the Markov chains in most of the aforementioned works are assumed to be homogeneous, 6-8 namely, the TPs are time-invariant. In reality, however, the switching of system mode is usually affected by multiple factors at the same time, and each factor may have different degree of influence on it at different times. For example, Markov chain can be an effective tool to describe networked delays, 9,10 and the variation rate of delays is affected by various factors at different times, such as poor quality of communication lines, network-loaded servers, and so on. Apparently, during the period of system operating, the network congestion and the condition of communication facilities are "persistently" varying. This phenomenon leads to the research of nonhomogeneous Markov chain, in which the transition probabilities are time-varying. In the existing control literature studies, the character of time-varying TPs is mainly divided into two categories: finite piecewise homogeneous and polyhedral. It is noteworthy that the finite piecewise homogeneous type of time-varying TPs is only a special case of polyhedral time-varying TPs. To investigate nonhomogeneous MJSs with polyhedral time-varying TPs, related works have been reported in recent years. The problem of stochastic stabilization for nonhomogeneous MJSs was first investigated in Reference 11. References 12 and 13 studied the problems of H ∞ control and output feedback control for nonhomogeneous 3982

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“…active power filter system [20]- [23], and chaotic systems [24]. dynamical system [25] To suppress the steady-state error, introducing an integer order integral term into the sliding surface is a good approach, which has been studied sufficiently. However, the fractional order integral provides the controller design with more degree of freedom, so it is more flexible.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Adaptive Sliding Mode Control System of Micro Gyroscope

Chen

Fei

2019

IEEE Access

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In this paper, an adaptive sliding mode control method based on fractional order method is proposed for the estimation of unknown parameters in micro gyroscope system. Firstly, compared with the traditional integer order sliding surface, the fractional order sliding surface in this paper increases the order terms which can adjust the fractional order, and improve the control performance and precision. Additionally, the adaptive laws are derived to tune the control parameters online based on the Lyapunov stability theorem to deal with the uncertainty of the system. Moreover, simulation results show that the proposed control system's convergence speed, output signal tracking error and parameter fitting are better than the integral sliding mode control system, proving that the proposed control method is practicable and effective. INDEX TERMS Fractional order, adaptive control, sliding mode control, micro gyroscope.

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H_∞ Filtering for Nonhomogeneous Markovian Jump Repeated Scalar Nonlinear Systems With Multiplicative Noises and Partially Mode-Dependent Characterization

Cited by 40 publications

References 53 publications

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

Robust finite‐time H_∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

Fractional Order Adaptive Sliding Mode Control System of Micro Gyroscope

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H∞ Filtering for Nonhomogeneous Markovian Jump Repeated Scalar Nonlinear Systems With Multiplicative Noises and Partially Mode-Dependent Characterization

Cited by 40 publications

References 53 publications

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

Fractional Order Adaptive Sliding Mode Control System of Micro Gyroscope

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Product

Resources

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H_∞ Filtering for Nonhomogeneous Markovian Jump Repeated Scalar Nonlinear Systems With Multiplicative Noises and Partially Mode-Dependent Characterization

Robust finite‐time H_∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case