Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices

Automatica ◽  
2011 ◽  
Vol 47 (1) ◽  
pp. 79-84 ◽  
Author(s):  
Yan Zhang ◽  
Yong He ◽  
Min Wu ◽  
Jie Zhang
Keyword(s):  
Partial Information ◽  
Transition Probability ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Jump Systems

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate 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.

Static anti-windup design for a class of Markovian jump systems with partial information on transition rates

2015 ◽  
Vol 26 (11) ◽  
pp. 2418-2435 ◽  
Author(s):  
Yunliang Wei ◽  
Wei Xing Zheng ◽  
Shengyuan Xu
Keyword(s):  
Partial Information ◽  
Markovian Jump Systems ◽  
Transition Rates ◽  
Markovian Jump ◽  
Jump Systems

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.

H∞control for discrete-time Markovian jump systems with partial information on transition probabilities

2013 ◽  
pp. n/a-n/a ◽  
Author(s):  
Yan Zhang ◽  
Yong He ◽  
Min Wu ◽  
Jie Zhang
Keyword(s):  
Discrete Time ◽  
Partial Information ◽  
Transition Probabilities ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Jump Systems
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