Stochastic input-to-state stability of switched stochastic nonlinear systems

Zhao, Ping; Feng, Wei; Kang, Yu

doi:10.1016/j.automatica.2012.06.058

Cited by 128 publications

(73 citation statements)

References 25 publications

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“…Pre-multiplying and post-multiplying the matrix on both sides of (38) by diag{P −1 1 , P −1 2 , Q −1 , I , Q −1 , P −1 1 , P −1 2 , I }, we get that (38) is equivalent to (37).…”

Section: Design Of Repetitive Controllermentioning

confidence: 99%

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Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

Shao

Huang

Xiang

2014

Circuits Syst Signal Process

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This paper investigates the problem of robust H ∞ repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with H ∞ performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate the effectiveness of the proposed method.

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Section: Design Of Repetitive Controllermentioning

confidence: 99%

“…Thus, stochastic systems have attracted great attention during the past several decades [5,11,18,36]. Some results on stochastic switched systems have been presented in [1,9,38]. In addition, time-delay phenomenon exists in many kinds of engineering and biological systems [26,31,32], such as mechanics, chemistry, physics, and economics.…”

Section: Introductionmentioning

confidence: 99%

Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

Shao

Huang

Xiang

2014

Circuits Syst Signal Process

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“…In addition, there is H ∞ filtering problem reported for a class of special nonlinear systems [38,39]. In [38], the H ∞ filtering problem was considered for a class of stochastic nonlinear systems with time-delay and the nonlinear term satisfying a Lipschitz constraint.…”

Section: Introductionmentioning

confidence: 99%

“…In [38], the H ∞ filtering problem was considered for a class of stochastic nonlinear systems with time-delay and the nonlinear term satisfying a Lipschitz constraint. We know that a T-S fuzzy system is a systematic representation for general nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

et al. 2014

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This paper considers the H ∞ filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e λt -weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e λt -weighted iISSiM and the H ∞ attenuation level from disturbance to estimation error is below a prescribed scalar. A set of sufficient conditions for the solvability of the H ∞ filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper.

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“…In particular, [19] and [20] addressed sufficient conditions of stochastic input-to state stability for nonlinear systems combined with Lyapunov theory; weighted fuzzy observer was proposed for discretetime nonlinear systems based on this property; [22] solved filtering problem for stochastic T-S fuzzy plants with timevarying delays with the aid of stochastic input-to-state stability. Therefore, the research of stochastic input-to-state stabilitybased robust fault reconstruction is of great meaning for stochastic nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Robust fault estimation for stochastic Takagi-Sugeno fuzzy systems

Liu

Binns

Shao

2016

IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society

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Abstract-Nowadays, industrial plants are calling for highperformance fault diagnosis techniques to meet stringent requirements on system availability and safety in the event of component failures. This paper deals with robust fault estimation problems for stochastic nonlinear systems subject to faults and unknown inputs relying on Takagi-Sugeno fuzzy models. Augmented approach jointly with unknown input observers for stochastic Takagi-Sugeno models is exploited here, which allows one to estimate both considered faults and full system states robustly. The considered unknown inputs can be either completely decoupled or partially decoupled by observers. For the un-decoupled part of unknown inputs, which still influence error dynamics, stochastic input-to-state stability properties are applied to take nonzero inputs into account and sufficient conditions are achieved to guarantee bounded estimation errors under bounded unknown inputs. Linear matrix inequalities are employed to compute gain matrices of the observer, leading to stochastic input-to-state-stable error dynamics and optimization of the estimation performances against un-decoupled unknown inputs. Finally, simulation on wind turbine benchmark model is applied to validate the performances of the suggested fault reconstruction methodologies.

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Stochastic input-to-state stability of switched stochastic nonlinear systems

Cited by 128 publications

References 25 publications

Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

Robust fault estimation for stochastic Takagi-Sugeno fuzzy systems

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