scholarly journals Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Lianglin Xiong ◽  
Xiaobing Zhou ◽  
Jie Qiu ◽  
Jing Lei
Keyword(s):  
Partial Information ◽  
Transition Probabilities ◽  
Mixed Delays ◽  
Transition Rates ◽  
Neutral Systems ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Analysis Technique ◽  
Transition Rate Matrix ◽  
Delay Dependent

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

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.

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