title: L1/ℓ1-Gain analysis and synthesis of Markovian jump positive systems with time delay.
abstract: This paper is concerned with stability analysis and control synthesis of Markovian jump positive systems with time delay. The notions of stochastic stability with L1- and ℓ1-gain performances are introduced for continuous- and discrete-time contexts, respectively. Using a stochastic copositive Lyapunov function, sufficient conditions for the stability with L1/ℓ1-gain performance of the systems are established. Furthermore, mode-dependent controllers are designed to achieve the stabilization with L1/ℓ1-gain of the resulting closed-loop systems. All proposed conditions are formulated in terms of linear programming. Numerical examples are provided to verify the effectiveness of the findings of theory.
authors.affiliation: Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China.
authors.forename: Junfeng
authors.initials: J
authors.lastname: Zhang
authors.affiliation: College of Engineering, Bohai University, Jinzhou 121013, China; Chongqing SANY Highintelligent Robots Co. Ltd., Chongqing 401120, People׳s Republic of China. Electronic address: xdzhaohit@gmail.com.
authors.forename: Xudong
authors.initials: X
authors.lastname: Zhao
authors.affiliation: School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Fubo
authors.initials: F
authors.lastname: Zhu
authors.affiliation: School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Zhengzhi
authors.initials: Z
authors.lastname: Han
keywords: Markovian jump positive systems; Stabilization; Stochastic copositive Lyapunov functional