Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion

Zhang, Weihai; Zhang, Huanshui; Chen, Bor‐Sen

doi:10.1109/tac.2008.929368

Cited by 167 publications

(146 citation statements)

References 25 publications

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“…Zhang and Chen [16] introduced the exact observability for stochastic Itô systems, while the exact detectability was, respectively, defined in [14] and [17]. In [6], the authors gave the notions of W-observability and W-detectability for Markov jump linear systems without multiplicative noise, where several equivalent conditions were derived.…”

Section: Exact Observability and Exact Detectabilitymentioning

confidence: 99%

“…In recent years, these concepts have been extended to stochastic linear systems [6,9,14,16−17] . In [14,[16][17], the authors introduced the exact observability and detectability of stochastic Itô-systems without jump parameters. Costa and Vol [6] dealt with similar topic to that of the present paper for the jump linear system without multiplicative noises.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, for system (3)-(4), we define " exact observability" and "exact detectability", which are extensions of [13,[16][17]. The operator spectrum technique is used to prove stochastic PBH Criteria for exact observability and exact detectability, which are based on some coupled generalized Lyapunov equations (GLEs) satisfied by E[x(t)x T (t)I {θ(t)=i} ].…”

Section: Introductionmentioning

confidence: 99%

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On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

Zhang

Fang

2010

J Syst Sci Complex

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This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Itô type with multiplicative noise (for short, MJLSS). Stochastic Popov-Belevith-Hautus (PBH) Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.

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Section: Exact Observability and Exact Detectabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

Zhang

Fang

2010

J Syst Sci Complex

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“…Stochastic noise is ubiquitous [14][15][16] and stochastic delay differential systems (SDDSs) have been one of the focuses of scientific research for many years. Many properties of SDDSs have been studied and lots of papers were published; see [17,18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance

Wang

Yang

Ding

et al. 2015

Mathematical Problems in Engineering

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This paper considers the -moment boundedness of nonlinear impulsive stochastic delay differential systems (ISDDSs). Using the Lyapunov-Razumikhin method and stochastic analysis techniques, we obtain sufficient conditions which guarantee the -moment boundedness of ISDDSs. Two cases are considered, one is that the stochastic delay differential system (SDDS) may not be bounded, and how an impulsive strategy should be taken to make the SDDS be bounded. The other is that the SDDS is bounded, and an impulsive disturbance appears in this SDDS, then what restrictions on the impulsive disturbance should be adopted to maintain the boundedness of the SDDS. Our results provide sufficient criteria for these two cases. At last, two examples are given to illustrate the correctness of our results.

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“…These important concepts of stochastic Itô systems have attracted much attention [6][7][8][9]13]. Recently, stochastic stability and stabilization by using the method of generalized Lyapunov equation (GLE) was presented in [8], which extended the deterministic theory to stochastic cases.…”

Section: Introductionmentioning

confidence: 99%

Critical stability and stabilization of discrete-time stochastic systems and its applications

Sun

Zhang

2011

Int. J. Control Autom. Syst.

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In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-BelevitchHautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.

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Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion

Cited by 167 publications

References 25 publications

On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance

Critical stability and stabilization of discrete-time stochastic systems and its applications

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