Title :
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
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;
Journal_Title :
Circuits and Systems II: Express Briefs, IEEE Transactions on
DOI :
10.1109/TCSII.2015.2433371
