Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems

Mao, Weihua; Deng, Feiqi; Wan, Anhua

doi:10.1007/s11432-015-5386-7

Cited by 31 publications

(11 citation statements)

References 34 publications

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“…It is well known (see [14]) that ζ i − t has the exponential probability distribution with parameter −γ ii . Hence, = 1 − e γiiv 1 − e −γv (6) as desired.…”

Section: Preliminaries and Notationmentioning

confidence: 83%

“…In recent years, stochastic systems have been considered by many researchers since many practical systems can be modeled using these kinds of systems. Many significant results for stochastic systems have been reported (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). Markovian jump systems are a special class of hybrid stochastic systems, which can be found in some engineering systems including power systems, manufacturing systems, ecosystems, and so forth.…”

Section: Introductionmentioning

confidence: 99%

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Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

Song

Zheng

et al. 2018

Sci. China Inf. Sci.

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Although the mean square stabilization of hybrid systems by feedback control based on discretetime observations of state and mode has been studied by several authors since 2013, the corresponding almost sure stabilization problem has received little attention. Recently, Mao was the first to study the almost sure stabilization of a given unstable systemẋ(t) = f (x(t)) by a linear discrete-time stochastic feedback control Ax([t/τ ]τ)dB(t) (namely the stochastically controlled system has the form dx(t) = f (x(t))dt + Ax([t/τ ]τ)dB(t)), where B(t) is a scalar Brownian, τ > 0, and [t/τ ] is the integer part of t/τ. In this paper, we consider a much more general problem. That is, we study the almost sure stabilization of a given unstable hybrid systemẋ(t) = f (x(t), r(t)) by nonlinear discrete-time stochastic feedback control u(x([t/τ ]τ), r([t/τ ]τ))dB(t) (so the stochastically controlled system is a hybrid stochastic system of the form dx(t) = f (x(t), r(t))dt + u(x([t/τ ]τ), r([t/τ ]τ))dB(t)), where B(t) is a multi-dimensional Brownian motion and r(t) is a Markov chain.

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“…It is well known (see [14]) that ζ i − t has the exponential probability distribution with parameter −γ ii . Hence, = 1 − e γiiv 1 − e −γv (6) as desired.…”

Section: Preliminaries and Notationmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

Song

Zheng

et al. 2018

Sci. China Inf. Sci.

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“…In this paper, the H − / H ∞ FDF design for Itô‐type affine nonlinear stochastic systems and quasi‐linear systems have been discussed, and sufficient conditions for the existence of the desired FDF have been given via HJIs and LMIs, respectively. The key to the FDF design of affine nonlinear stochastic systems is how to solve the coupled HJIs, this is a very challenging problem, and some potential effective approaches to overcome this difficulty may refer to [45,46] for global linearization method, [47] for neural network method, and [20] for fuzzy interpolation method. In addition, from our simulation example, in order to select a more suitable combination of ( γ , δ ), a co‐design algorithm for H − index and H ∞ index is necessary.…”

Section: Resultsmentioning

confidence: 99%

“…where F i (0) = 0, i = 1, 2. As a matter of fact, in (25), if one takes g 1 (x) = B 0 , h 1 (x) = C 0 ,…”

Section: Lmi-based Approach For Quasi-linear Systemsmentioning

confidence: 99%

Fault detection filtering for Itô‐type affine nonlinear stochastic systems

Zhang

Deng

Zhang

et al. 2019

Asian Journal of Control

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This paper studies the mixed H − /H ∞ fault detection filtering of Itô-type nonlinear stochastic systems. Mixed H − /H ∞ filtering combines the system robustness to the external disturbance and the sensitivity to the fault of the residual signal. Firstly, for Itô-type affine nonlinear stochastic systems, some sufficient criteria are obtained for the existence of H − /H ∞ filter in terms of Hamilton-Jacobi inequalities (HJIs). Secondly, for a class of quasi-linear Itô systems, a sufficient condition is given for the existence of H − /H ∞ filter by means of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.

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“…Many stochastic systems which not only depend on present and past states but also involve derivatives with delays are modeled by neutral stochastic differential delay equations (NSDDEs). Although extensive literature can be found in this area, we mention a few of them herein [16][17][18][19][20][21][22][23]. Also, many researchers have made efforts in regard to the stability of highly nonlinear neutral stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays

Shen

Fei

et al. 2019

Sci. China Inf. Sci.

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This paper reports the boundedness and stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) with multiple delays. Without imposing linear growth condition, the boundedness and exponential stability of the exact solution are investigated by Lyapunov functional method. In particular, using the M-matrix technique, the mean square exponential stability is obtained. Finally, three examples are presented to verify our results.

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Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems

Cited by 31 publications

References 34 publications

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

Fault detection filtering for Itô‐type affine nonlinear stochastic systems

Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays

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