Robust control of descriptor discrete-time Markovian jump systems

Lam, James; Shu, Zhan; Xu, Shengyuan; Boukas, El‐Kébir

doi:10.1080/00207170600999322

Cited by 161 publications

(105 citation statements)

References 19 publications

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“…which implies that S i is nonsingular and also ensures the existence of parameter matrices G i , K i , L i and M i in (18). The proof is completed.…”

Section: Resultsmentioning

confidence: 62%

“…Recall the following definition of mean square stability for MJSs. Definition 1 [18,19] System (7) with ζ k = 0 is said to be mean square stable if…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…The parameters of the sub-optimal robust fault detection filter can be determined by (18), and the suboptimal robust H ∞ attenuation level for fault detection dynamics is given by γ * = γ 2 opt , where γ 2 opt are the sub-optimal solution of the corresponding convex optimization problem.…”

Section: Remarkmentioning

confidence: 99%

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Robust fault detection for networked systems with communication delay and data missing

2009

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In this paper, the robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which are typically resulted from the limited capacity of the communication networks. Network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but reside in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties as well as incomplete measurements, the error between residual and fault is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust H∞ filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique.

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“…which implies that S i is nonsingular and also ensures the existence of parameter matrices G i , K i , L i and M i in (18). The proof is completed.…”

Section: Resultsmentioning

confidence: 62%

“…Recall the following definition of mean square stability for MJSs. Definition 1 [18,19] System (7) with ζ k = 0 is said to be mean square stable if…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

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Robust fault detection for networked systems with communication delay and data missing

2009

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“…Finally, an illustrative simulation example has been given to illustrate the effectiveness of the proposed design method. One of the future research topics would be to extend the present results to more complex systems such as descriptor systems and Markovian jump systems [41]. …”

Section: Discussionmentioning

confidence: 99%

Non‐fragile H _∞ control with randomly occurring gain variations, distributed delays and channel fadings

Wang

Ding

et al. 2015

IET Control Theory & Applications

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This paper is concerned with the non-fragile H ∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H ∞ output-feedback controller such that the closed-loop control system is stochastically stable with a prescribed H ∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H ∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimization problem solvable via the semi-definite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method.

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“…During the past decades, many issues on MJLSs such as stability and stabilization, H ∞ control and filtering, optimal tracking, have been well investigated [6,8,9,14,16] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Non-fragile sampled data H∞ filtering of general continuous Markov jump linear

Shen¹,

Zhang²,

Yuan³

et al. 2014

Kybernetika

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Robust control of descriptor discrete-time Markovian jump systems

Cited by 161 publications

References 19 publications

Robust fault detection for networked systems with communication delay and data missing

Robust fault detection for networked systems with communication delay and data missing

Non‐fragile H _∞ control with randomly occurring gain variations, distributed delays and channel fadings

Non-fragile sampled data H∞ filtering of general continuous Markov jump linear

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Robust control of descriptor discrete-time Markovian jump systems

Cited by 161 publications

References 19 publications

Robust fault detection for networked systems with communication delay and data missing

Robust fault detection for networked systems with communication delay and data missing

Non‐fragile H ∞ control with randomly occurring gain variations, distributed delays and channel fadings

Non-fragile sampled data H∞ filtering of general continuous Markov jump linear

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Non‐fragile H _∞ control with randomly occurring gain variations, distributed delays and channel fadings