Mean Stability of Positive Markov Jump Linear Systems With Homogeneous and Switching Transition Probabilities

Author

Jie Lian ; Jiao Liu ; Yan Zhuang

Author_Institution

Fac. of Electron. Inf. & Electr. Eng., Dalian Univ. of Technol., Dalian, China

Volume

62

Issue

8

fYear

2015

fDate

Aug. 2015

Firstpage

801

Lastpage

805

Abstract

This brief investigates the mean stability problem of positive Markov jump linear systems (PMJLSs) in the discrete- time domain. First, some sufficient and necessary conditions are presented for PMJLSs with homogeneous transition probability (TP) by analyzing the time evolution of the first-order moment of the state. Then, by using a copositive Lyapunov function approach, a computable sufficient condition for the PMJLSs with switching TPs is proposed in the framework of dwell time to guarantee the mean stability. Finally, some numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

Keywords

Lyapunov methods; Markov processes; electrical conductivity transitions; linear systems; probability; switching systems (control); Lyapunov function; PMJLS; discrete- time domain; mean stability; positive Markov jump linear systems; switching transition probability; time evolution; Asymptotic stability; Circuit stability; Circuits and systems; Linear systems; Markov processes; Stability analysis; Switches; Copositive Lyapunov function; Homogeneous and switching TPs; Mean stability; Positive Markov jump linear systems; Time-dependent switching; homogeneous and switching transition probabilities (TPs); mean stability; positive Markov jump linear systems (PMJLSs); time-dependent switching;

fLanguage

English

Journal_Title

Circuits and Systems II: Express Briefs, IEEE Transactions on

Publisher

ieee

ISSN

1549-7747

Type

jour

DOI

10.1109/TCSII.2015.2433371

Filename

7107994