Mean stability of continuous-time semi-Markov jump linear positive systems

Author

Ogura, M. ; Martin, Clyde F.

Author_Institution

Dept. of Math. & Stat., Texas Tech Univ., Lubbock, TX, USA

fYear

2014

fDate

4-6 June 2014

Firstpage

3261

Lastpage

3266

Abstract

In this paper we study the mean stability of continuous-time semi-Markov jump linear positive systems, which are switched linear systems such that their state variables are in positive orthants and their switching signal is a Markov renewal process. The main result of this paper shows that the mean stability is determined by the spectral radius of a matrix. In the proof we utilize a stability-preserving discretization of continuous-time semi-Markov jump linear systems. The obtained results are demonstrated through the stability analysis and the stabilization of linear time-invariant systems with controller failures.

Keywords

Markov processes; continuous time systems; invariance; linear systems; matrix algebra; stability; time-varying systems; Markov renewal process; continuous-time semiMarkov jump linear positive systems; controller failures; linear time-invariant system stabilization; matrix; mean stability; spectral radius; stability-preserving discretization; state variables; switched linear systems; switching signal; Linear systems; Markov processes; Stability criteria; Switches; Markov processes; Stability of hybrid systems; Switched systems;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2014

Conference_Location

Portland, OR

ISSN

0743-1619

Print_ISBN

978-1-4799-3272-6

Type

conf

DOI

10.1109/ACC.2014.6859013

Filename

6859013