Stability and control for linear systems with jump Markov perturbations

Morozan, Toader

doi:10.1080/07362999508809384

Cited by 62 publications

(43 citation statements)

References 8 publications

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“…In addition, we give sufficient conditions for the convergence of the feedforward term, and when it converges we provide an explicit formula for its computation. In contrast to our work, where we assume that the reference is deterministic and known for the entire future, the authors of [35], [36], [37] have investigated tracking and the effects of perturbations, for the case where the reference or perturbation is a Markov process subject to causal processing. Subsequently, we give a short survey, of the state of the art in the design of optimal controllers of Markovian jump linear systems.…”

Section: A Survey Of Related Resultsmentioning

confidence: 99%

Optimal Preview Control of Markovian Jump Linear Systems

Running

Martins

2009

IEEE Trans. Automat. Contr.

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Isr develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government.Isr is a permanent institute of the university of maryland, within the a. James clark school of engineering. It is a graduated national science foundation engineering research center. AbstractIn this paper, we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview (reference look-ahead). For a quadratic cost and given a reference sequence, we obtain the optimal solution for the full information case. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term. We show that the feedback term is identical to the standard optimal linear quadratic regulator for Markovian jump linear systems. We provide explicit formulas for computing the feedforward term, including an analysis of convergence.

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Section: A Survey Of Related Resultsmentioning

confidence: 99%

Optimal Preview Control of Markovian Jump Linear Systems

Running

Martins

2009

IEEE Trans. Automat. Contr.

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“…Research into this class of systems and their applications span several decades [3][4][5]. Basic results on jumping linear quadratic control (JLQC) theory can be found in References [6][7][8][9][10]. For some representative related work on this general topic, we refer the reader to References [6,1,2,[11][12][13][14][15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Robust stability, stabilization and ℋ_∞ control of time‐delay systems with Markovian jump parameters

Mahmoud

Shi

2003

Intl J Robust & Nonlinear

115

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SUMMARYIn this paper, the problems of stochastic stability and stabilization for a class of uncertain time-delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process. The parametric uncertainties are assumed to be real, timevarying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factor is constant and unknown with a known bound. Complete results for both delay-independent and delay-dependent stochastic stability criteria for the nominal and uncertain time-delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed H 1 -performance are guaranteed. We establish that the control problem for the time-delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided.

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“…For some representative work on this general topic, we refer the reader to [3,[7][8][9][12][13][14][15]26] and the references therein. Some recent results can be found in [1,2,[4][5][6]10,[16][17][18][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Stochastic stability of linear systems with semi-Markovian jump parameters

2005

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Over the past two decades considerable effort has been devoted to problems of stochastic stability, stabilisation, filtering and control for linear and nonlinear systems with Markovian jump parameters, and a number of results have been achieved. However, due to the exponential distribution of the Markovian chain, there are many restrictions on existing results for practical applications. In the present paper, we study systems whose jump parameters are semi-Markovian rather than fully Markovian. We consider only linear systems with semi-Markovian jump parameters, and also study systems with phase-type semi-Markovian jump parameters, because the family of phase-type distributions is dense in the families of all probability distributions on [0, +00). Some stochastic stability results are obtained. An example is given to show the potential of the proposed techniques.

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Stability and control for linear systems with jump Markov perturbations

Cited by 62 publications

References 8 publications

Optimal Preview Control of Markovian Jump Linear Systems

Optimal Preview Control of Markovian Jump Linear Systems

Robust stability, stabilization and ℋ_∞ control of time‐delay systems with Markovian jump parameters

Stochastic stability of linear systems with semi-Markovian jump parameters

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Stability and control for linear systems with jump Markov perturbations

Cited by 62 publications

References 8 publications

Optimal Preview Control of Markovian Jump Linear Systems

Optimal Preview Control of Markovian Jump Linear Systems

Robust stability, stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters

Stochastic stability of linear systems with semi-Markovian jump parameters

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Robust stability, stabilization and ℋ_∞ control of time‐delay systems with Markovian jump parameters