Zhang Junfeng, Zhao Xudong, Zhu Fubo, Han Zhengzhi
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.
ISA Trans. 2016 Jul;63:93-102. doi: 10.1016/j.isatra.2016.03.015. Epub 2016 Apr 7.
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.
本文关注具有时滞的马尔可夫跳跃正系统的稳定性分析与控制综合。分别针对连续时间和离散时间情形，引入了具有(L_1)和(\ell_1)增益性能的随机稳定性概念。利用一个随机余正定李雅普诺夫函数，建立了系统具有(L_1 / \ell_1)增益性能的稳定性充分条件。此外，设计了依赖模式的控制器，以实现所得闭环系统的(L_1 / \ell_1)增益稳定。所有提出的条件都以线性规划的形式给出。提供了数值例子来验证理论结果的有效性。
