Stability Analysis for Time-Delay Markovian Jump Systems with Partial Information on Transition Probabilities

2018 ◽  
Author(s):  
Yan Zhang ◽  
Ke Lou ◽  
Shilin Liu ◽  
Mingjun Han ◽  
Yuan Ge
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Partial Information ◽  
Transition Probabilities ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Jump Systems

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.

scholarly journals Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Dan Ye ◽  
Quan-Yong Fan ◽  
Xin-Gang Zhao ◽  
Guang-Hong Yang
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Transition Probability Matrix ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Delay Dependent ◽  
Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

Finite-time H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities

2013 ◽  
Vol 91 (12) ◽  
pp. 1020-1028 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Guihua Li
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Partial Information ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Partly Unknown Transition Probabilities ◽  
Stability And Stabilization ◽  
Jump Systems

This paper addresses the problems of finite-time stochastic stability and stabilization for linear Markovian jump systems subject to partial information on the transition probabilities. By introducing bounded finite time and stochastic character, sufficient conditions that can ensure bounded finite time and H∞ finite-time bounded filtering are derived. Finally, an example is given to illustrate the efficiency of the proposed method.

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