Robust control for Markovian jumping discrete-time systems

Shi, Peng; Boukas, El‐Kébir; Agarwal, Ramesh K.

doi:10.1080/002077299291912

Cited by 50 publications

(40 citation statements)

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“…This is in contrast with existing approaches of H ∞ control of MJL systems, such as those of Costa and do Val (1996), Fragoso et al (1995), and Shi et al (1999), which require the jumping parameter to be accessible.…”

Section: Problem Formulationcontrasting

confidence: 42%

“…This is in contrast with existing robust H ∞ control results for MJL systems, such as those of Boukas and Liu (2001) and Shi et al (1999), which are based on Lyapunov functions that are independent of the system uncertain parameters and require the jumping parameter to be accessible.…”

Section: Robust H ∞ Controlmentioning

confidence: 47%

“…In particular with regard to H ∞ control of discrete-time MJL systems, state-feedback control have been studied in, for instance, Costa and do Val (1996) and Fragoso et al (1995), whereas robust H ∞ control schemes have been proposed in, e.g. Boukas and Liu (2001) and Shi et al (1999). A common feature of the existing H ∞ control methods is that the jumping parameter is assumed to be accessible and is required for the implementation of the controller, which is a MJL system as well.…”

Section: Introductionmentioning

confidence: 99%

“…This class of systems is very appropriate to model plants whose structure is subject to random abrupt changes due to, for instance, random component failures, abrupt environment disturbance, changes of the operating point of a linearized model of a nonlinear system, etc. A number of control problems related to discretetime MJL systems has been analysed by several authors; see, for instance, Blair and Sworder (1975), Boukas and Liu (2001), Costa and do Val (1996), Costa and Fragoso (1993), Costa and Marques (2000), Fragoso (1989), Fragoso et al (1995), Ji and Chizeck (1990), Ji et al (1991), Morozan (1983), Shi et al (1999), Wonham (1970) and the references therein. In particular with regard to H ∞ control of discrete-time MJL systems, state-feedback control have been studied in, for instance, Costa and do Val (1996) and Fragoso et al (1995), whereas robust H ∞ control schemes have been proposed in, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Mode-Independent H∞ Control of Discrete-Time Markovian Jump Linear Systems

Souza

2005

IFAC Proceedings Volumes

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This paper addresses the problem of H ∞ control of discrete-time linear systems with Markovian jumping parameters. The main contribution of the paper is to provide a method for designing a state-feedback H ∞ control for systems where the jumping parameter is not accessible. The cases where the transition probability matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust H ∞ control problem for systems with polytopic-type uncertain state-space model matrices is also considered and a state-feedback control design based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed control designs are given in terms of linear matrix inequalities. Illustrative numerical examples are provided to demonstrate the effectiveness of the derived results. Copyright

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Section: Problem Formulationcontrasting

confidence: 42%

Section: Robust H ∞ Controlmentioning

confidence: 47%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mode-Independent H∞ Control of Discrete-Time Markovian Jump Linear Systems

Souza

2005

IFAC Proceedings Volumes

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“…Note that when only failure process Z k exists and the failure detection and isolation scheme is perfect, i.e. S ¼ f1g; the results here will cover that in the work of Shi et al [29]. In particular, if S ¼ f1g and Z ¼ f1g; Theorem 3.1 will reduce to the standard quadratic stability concept, see for e.g.…”

Section: Robust Control Resultsmentioning

confidence: 92%

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Shi

Boukas

Nguang

et al. 2003

Optim Control Appl Methods

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SUMMARYThe problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique.

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An application of robust control technique to manufacturing systems with uncertain processing time

Boukas

Shi

Agarwal

2000

Optim Control Appl Methods

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SUMMARYThis paper studies the inventory control problem for a production system with uncertain processing time and delay in control. First, the stabilization of the delayed system is analysed. Then, a controller is designed such that a disturbance attenuation of the system is achieved. The problem of robust control of the system with parametric uncertainty is also investigated. Linear matrix inequality approach is employed to solve the above problems. A numerical example is given to show the potential of the proposed techniques.

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Robust control for Markovian jumping discrete-time systems

Cited by 50 publications

References 0 publications

Mode-Independent H∞ Control of Discrete-Time Markovian Jump Linear Systems

Mode-Independent H∞ Control of Discrete-Time Markovian Jump Linear Systems

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

An application of robust control technique to manufacturing systems with uncertain processing time

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