scholarly journals Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions

2010 ◽  
Vol 55 (7) ◽  
pp. 1695-1701 ◽  
Author(s):  
Lixian Zhang ◽  
James Lam
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems ◽  
Analysis And Synthesis ◽  
Necessary And Sufficient

Nonfragile H∞ Filtering of Continuous Markov Jump Linear Systems With General Transition Probabilities

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Mouquan Shen ◽  
Guang-Hong Yang
Keyword(s):  
Linear Systems ◽  
Filter Design ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems ◽  
Stochastically Stable

This paper concerns the mode dependent H∞ filter design for continuous Markov jump linear systems. The filter gain to be designed is assumed to have additive variations and the transition probabilities are allowed to be known, uncertain with known bounds and unknown. Attention is focused on the design of a mode dependent nonfragile full order filter, which guarantees the filtering error system to be stochastically stable and has a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the desired filter design are given in the framework of linear matrix inequality. If the filter gain variations become zero and the transition probabilities are completely known, the proposed method is reduced to the standard H∞ filtering results. A numerical examples is given to show the effectiveness of the proposed method.

Stochastic stability of positive Markov jump linear systems with completely/partially known transition rates

2018 ◽  
Vol 40 (9) ◽  
pp. 2724-2731 ◽  
Author(s):  
Ying Chen ◽  
Yuming Bo ◽  
Baozhu Du
Keyword(s):  
Linear Programming ◽  
Linear Systems ◽  
Stochastic Stability ◽  
Sufficient Condition ◽  
Transition Rates ◽  
Necessary And Sufficient Condition ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems ◽  
Necessary And Sufficient

This paper addresses the stochastic stability problem of positive Markov jump linear systems (PMJLSs). A necessary and sufficient condition of stochastic stability for PMJLSs is given which can be checked by solving linear programming feasibility problems due to the positivity property. A common co-positive Lyapunov function is constructed to solve the problem, and the equivalence among stochastic stability, 1-moment stability and exponential mean stability is proved afterwards. Considering the uncertain transition rates situation, PMJLSs with partially known transition rate matrix are investigated, and a necessary and sufficient condition for robust stochastic stability is proposed in linear programming form. Numerical examples are presented to show the effectiveness of the proposed results.

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