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ISA Trans. 2016 Jul;63:93-102. doi: 10.1016/j.isatra.2016.03.015. Epub 2016 Apr 7.

L1/ℓ1-Gain analysis and synthesis of Markovian jump positive systems with time delay.

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Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China.
College of Engineering, Bohai University, Jinzhou 121013, China; Chongqing SANY Highintelligent Robots Co. Ltd., Chongqing 401120, People׳s Republic of China. Electronic address:
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.


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.


Markovian jump positive systems; Stabilization; Stochastic copositive Lyapunov functional

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