Stability and stabilization for non-homogeneous positive Markovian jump linear systems

DOI编号  10.7641/CTA.2019.80909
2020,37(2):229-235

 作者 单位 E-mail 蒋鹏飞 中国科学技术大学 jpengfei@mail.ustc.edu.cn 朱进 中国科学技术大学 jinzhu@mail.ustc.edu.cn 奚宏生 中国科学技术大学

本文研究一类非齐次马尔可夫跳跃正线性系统的稳定与镇定问题. 该系统中模态的变化服从非齐次马尔可夫过程, 其模态转移速率/概率矩阵是随时间随机变化的, 且变化规律由一个高层马尔可夫过程描述, 本文提出一种双层马尔可夫跳跃正系统模型来刻画此类系统特征. 在此基础上, 利用切换线性余正李雅普诺夫函数给出此类连续和离散时间非齐次马尔可夫跳跃正线性系统平均稳定的判据. 然后, 运用线性规划方法设计依赖于模态-模态转移速率/概率矩阵的状态反馈控制器, 进而实现闭环系统的平均稳定性. 最后, 以功率分配系统为例给出仿真算例, 验证了所设计控制策略的有效性.

This paper focuses on the stability and stabilization problem for a class of non-homogeneous positive Markovian jump linear systems. The switching of system mode is governed by a non-homogeneous Markov process whose mode transition rates/probabilities matrix (MTRM/MTPM) is time-varying. Besides, the stochastic variation of MTRM/MTPM is governed by a high layer Markov process, then a two-layer Markovian jump model is proposed to characterize such system features. Based on such model, the mean stability criteria for continuous-time and discrete-time systems are given by designing switched linear co-positive Lyapunov functions. Then, a mode-MTRM/MTPM-dependent state feedback controller which can stabilize the closed loop system is designed through a linear programming method. Finally, the effectiveness of the proposed control strategy is verified by two numerical examples.