Stochastic stability of positive Markov jump linear systems with fixed dwell time. (May 2021)

• Record Type: Journal Article
• Authors: Lian, Jie; Wang, Renke
• Is Part Of: Nonlinear analysis. Volume 40(2021)
• Publication Date: 2021-05
• Subjects: Positive system -- Markov jump linear system -- Dwell time -- Partially known transition rate; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2021.101014
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper studies the stochastic stability of positive Markov jump linear systems with a fixed dwell time. By constructing an auxiliary system that originated from the initial system with state jumps, sufficient and necessary conditions of stochastic stability for positive Markov jump linear systems are obtained with both exactly known and partially known transition rates. The main idea in the latter case is applying a convex combination to convert bilinear programming into linear programming problems. On this basis, multiple piecewise linear co-positive Lyapunov functions are provided to achieve less conservative results. Then state feedback controller is designed to stabilize the positive Markov jump linear systems by solving linear programming problems. Numerical examples are presented to illustrate the viability of our conclusions.