H∞ fuzzy control for nonlinear time-delay singular Markovian jump systems with partly unknown transition rates

2014 ◽  
Vol 254 ◽  
pp. 106-125 ◽  
Author(s):  
Li Li ◽  
Qingling Zhang ◽  
Baoyan Zhu
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Markovian Jump Systems ◽  
Transition Rates ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Partly Unknown Transition Rates

scholarly journals H∞Fuzzy Control for Nonlinear Singular Markovian Jump Systems with Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Li Li ◽  
Qingling Zhang ◽  
Yi Zhang ◽  
Baoyan Zhu
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
State Feedback ◽  
The State ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stochastic Stabilization ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

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.

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

2012 ◽  
Vol 235 ◽  
pp. 254-258 ◽  
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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