51. Stochastic stability of positive Markov jump linear systems with completely/partially known transition rates.
- Author
-
Chen, Ying, Bo, Yuming, and Du, Baozhu
- Subjects
- *
MARKOVIAN jump linear systems , *STOCHASTIC analysis , *LINEAR programming , *LYAPUNOV functions , *EXPONENTIAL functions - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF