Stochastic Stability Analysis for Continuous Time Fault Tolerant Control Systems

Srichander, R.; Walker, Bruce K.

doi:10.23919/acc.1991.4791416

Cited by 45 publications

(102 citation statements)

References 15 publications

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“…To address the effects of imperfect FDI results, Markovian models are used to study the reliability evaluation problem for given FTCSs. Although the Markovian modeling of FDI may be restrictive, the influence of FDI imperfectness is directly tackled in this model (Mariton, 1989;Srichander and Walker, 1993;Mahmoud et al, 2003).…”

Section: Remarkmentioning

confidence: 99%

Reliability Modeling of Fault Tolerant Control Systems

Li¹,

Zhao²,

Yang³

2007

International Journal of Applied Mathematics and Computer Science

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This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined by four probabilistic parameters based on the Markovian model of FTCSs. Computed from the transition probabilities of the semi-Markov process, the reliability index incorporates control objectives, hard deadline, and the effects of imperfect FDI, a suitable quantitative measure of the overall performance.

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Section: Remarkmentioning

confidence: 99%

Reliability Modeling of Fault Tolerant Control Systems

Li¹,

Zhao²,

Yang³

2007

International Journal of Applied Mathematics and Computer Science

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“…The theory of stability, optimal control and H 2 /H ∞ control, as well as important applications of such systems, can be found in several papers in the current literature, for instance in [5,6,7,8,10,12,13,14,15,18,19] for continuous-time case, and [9] for the discrete-time case. Fault tolerant control issues were also considered in the same framework, for instance in [1,2,3,22,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Output feedback stochastic H_∞ stabilization of networked fault-tolerant control systems

Aberkane

Sauter

Ponsart

2007

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this paper, static output feedback stochastic stabilization and disturbance attenuation issues for a class of discrete-time Networked Control Systems (NCSs) subject to random failures and random delays are addressed. The different random processes are modeled as Markovian chains, and the resulting closed-loop system belongs to the class of discrete-time Markovian Jump Linear Systems (MJLS). Results are formulated as matrix inequalities. A numerical algorithm based on nonconvex optimization is provided and its running is illustrated on a classical example from literature.

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“…However, they either address the simpler case when θ(k) is an i.i.d. sequence [7], [8], use heuristic arguments [9], or employ sophisticated results [10]. To the best of our knowledge, there is no complete proof of the Markov nature of (x(k), θ(k)) for system (1), when θ(k) is a Markov chain.…”

Section: Introductionmentioning

confidence: 99%

On the Markov property for nonlinear discrete-time systems with Markovian inputs

Tejada

González

Gray

2006

2006 American Control Conference

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Abstract-The behavior of a general hybrid system in discrete-time can be represented by a non-linear difference equation, where θ(k) is assumed to be a finite-state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), θ(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only fundamental measure-theoretical concepts.

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Stochastic Stability Analysis for Continuous Time Fault Tolerant Control Systems

Cited by 45 publications

References 15 publications

Reliability Modeling of Fault Tolerant Control Systems

Reliability Modeling of Fault Tolerant Control Systems

Output feedback stochastic H_∞ stabilization of networked fault-tolerant control systems

On the Markov property for nonlinear discrete-time systems with Markovian inputs

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Stochastic Stability Analysis for Continuous Time Fault Tolerant Control Systems

Cited by 45 publications

References 15 publications

Reliability Modeling of Fault Tolerant Control Systems

Reliability Modeling of Fault Tolerant Control Systems

Output feedback stochastic H∞ stabilization of networked fault-tolerant control systems

On the Markov property for nonlinear discrete-time systems with Markovian inputs

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Output feedback stochastic H_∞ stabilization of networked fault-tolerant control systems