Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities

Zhang, Lixian; Boukas, El‐Kébir

doi:10.3182/20080706-5-kr-1001.02620

Cited by 115 publications

(180 citation statements)

References 6 publications

Supporting

Mentioning

177

Contrasting

Unclassified

Order By: Relevance

“…Two numerical examples were given to show the effectiveness of the method. Future work will investigate the synchronization problem over a network with mode-dependent mixed time delays for Markovian jump master-slave systems (see more details in [15]- [16], [24] and [42]). …”

Section: Coclusionmentioning

confidence: 99%

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Karimi

2012

Journal of the Franklin Institute

273

114

View full text Add to dashboard Cite

Abstract-In this paper, a sliding-mode approach is proposed for exponential H ∞ synchronization problem of a class of masterslave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent modedependent sliding mode exponential H ∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the  H synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.

show abstract

Section: Coclusionmentioning

confidence: 99%

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Karimi

2012

Journal of the Franklin Institute

273

114

View full text Add to dashboard Cite

show abstract

“…Stochastic method including Markovian chain was proposed in Refs. [5,19]. In paper [19], the stability and stabilization problems of a class of continuous-time and discrete-time Markovian jump linear system with partly unknown transition probabilities are investigated.…”

Section: Introductionmentioning

confidence: 99%

“…[5,19]. In paper [19], the stability and stabilization problems of a class of continuous-time and discrete-time Markovian jump linear system with partly unknown transition probabilities are investigated. In contrast with the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements.…”

Section: Introductionmentioning

confidence: 99%

“…The mixed mode dependent timedelays consist of both discrete and distributed delays. A more updated literature review of partly known probabilities in the Markov process can be states as [19,[51][52][53][54]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [19], the problem of stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities is investigated. In Ref.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

H∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains

Guo¹,

Zhang

2012

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

This paper is concerned with the problem of H 1 estimation for networked control systems. Time delays and packet dropouts are considered simultaneously. The occurrence probability of each time delay is considered. The packet dropouts have the Bernoulli distributions. The system is modeled as Markovian jump linear systems with partly unknown transition probability. State observer is designed to estimate the practical state with H 1 feature. The estimation problem is cast into a set of linear matrix inequalities. An example is provided to illustrate the effectiveness and applicability of the proposed method.

show abstract

Neural‐network‐based finite‐time H_∞ control for extended Markov jump nonlinear systems

Luan

Liu

Shi

2010

Adaptive Control & Signal

View full text Add to dashboard Cite

This paper presents a neural-network-based finite-time H ∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed-loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H ∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results.

show abstract

Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities

Cited by 115 publications

References 6 publications

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

H∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains

Neural‐network‐based finite‐time H_∞ control for extended Markov jump nonlinear systems

Contact Info

Product

Resources

About

Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities

Cited by 115 publications

References 6 publications

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

H∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

Contact Info

Product

Resources

About

Neural‐network‐based finite‐time H_∞ control for extended Markov jump nonlinear systems