Stabilization of Time-Delay Markovian Jump Systems via Probability Rate Synthesis and State Feedback

This paper investigates the problem ofH∞fuzzy control for a class of nonlinear singular Markovian jump systems with time delay. This class of systems under consideration is described by Takagi-Sugeno (T-S) fuzzy models. Firstly, sufficient condition of the stochastic stabilization by the method of the augmented matrix is obtained by the state feedback. And a designed algorithm for the state feedback controller is provided to guarantee that the closed-loop system not only is regular, impulse-free, and stochastically stable but also satisfies a prescribedH∞performance for all delays not larger than a given upper bound in terms of linear matrix inequalities. ThenH∞fuzzy control for this kind of systems is also discussed by the static output feedback. Finally, numerical examples are given to illustrate the validity of the developed methodology.

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Robust Finite-TimeH∞Control for Nonlinear Markovian Jump Systems with Time Delay under Partially Known Transition Probabilities

Abstract and Applied Analysis ◽

10.1155/2014/938781 ◽

2014 ◽

Vol 2014 ◽

pp. 1-16

Author(s):

Dong Yang ◽

Guangdeng Zong

Keyword(s):

Time Delay ◽

Finite Time ◽

State Feedback ◽

Transition Probabilities ◽

Feedback Stabilization ◽

Markovian Jump Systems ◽

Markovian Jump ◽

Finite Time Boundedness ◽

Jump Systems ◽

Nonlinear Markovian Jump Systems

This paper is concerned with the problem of robust finite-timeH∞control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. Firstly, for the nominal nonlinear Markovian jump systems, sufficient conditions are proposed to ensure finite-time boundedness,H∞finite-time boundedness, and finite-timeH∞state feedback stabilization, respectively. Then, a robust finite-timeH∞state feedback controller is designed, which, for all admissible uncertainties, guarantees theH∞finite-time boundedness of the corresponding closed-loop system. All the conditions are presented in terms of strict linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of all the results.

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Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2010.01601 ◽

2010 ◽

Vol 36 (11) ◽

pp. 1601-1610 ◽

Cited By ~ 9

Author(s):

Li MA ◽

Fei-Peng DA ◽

Ling-Yao WU

Keyword(s):

State Feedback ◽

Markovian Jump Systems ◽

Exponential Stabilization ◽

Time Varying ◽

Markovian Jump ◽

State Delays ◽

Delayed State Feedback ◽

Jump Systems

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Stochastic Admissibility for a Class of Nonlinear Singular Markovian Jump Systems with Time-Delay and Partially Unknown Transition Probabilities

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.235.254 ◽

2012 ◽

Vol 235 ◽

pp. 254-258 ◽

Cited By ~ 1

Author(s):

Shao Hua Long ◽

Shou Ming Zhong

Keyword(s):

Time Delay ◽

Transition Probabilities ◽

Functional Method ◽

Markovian Jump Systems ◽

Linear Matrix ◽

Markovian Jump ◽

Weighting Matrix ◽

Singular Markovian Jump Systems ◽

Jump Systems ◽

Stochastic Admissibility

The problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities is discussed in this note. The considered singular matrices Er(t) in the discussed system are mode-dependent. By using the free-weighting matrix method and the Lyapunov functional method, a sufficient condition which guarantees the considered system to be stochastically admissible is presented in the form of linear matrix inequalities(LMIs). Finally, a numerical example is given to show the effectiveness of the presented method.

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