Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

Zhai Ding; An Liwei; Li Jinghao; Zhang Qingling

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Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

机译：具有不完善转移概率的离散时间分段齐次马尔可夫跳跃线性系统的镇定

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This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

机译：本文致力于研究具有不完善转移概率的离散时间分段齐次马尔可夫跳跃线性系统的稳定性和稳定性问题。得出足够的条件以确保所考虑的系统是随机稳定的。此外，推导了存在依赖于模式和依赖于变化的状态反馈控制器的相应充分条件，以保证闭环系统的随机稳定性，并进一步提出了一种新的方法来设计静态输出反馈控制器。引入额外的松弛矩阵变量以消除对Lyapunov矩阵的方程约束。最后，通过一些数值例子说明了所提方法的有效性。

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来源
《Mathematical Problems in Engineering》 |2015年第6期|720353.1-720353.14|共14页
作者
Zhai Ding; An Liwei; Li Jinghao; Zhang Qingling;
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Northeastern Univ, Coll Sci, Shenyang 110819, Peoples R China.;

Northeastern Univ, Coll Sci, Shenyang 110819, Peoples R China.;

Northeastern Univ, Coll Sci, Shenyang 110819, Peoples R China.;

Northeastern Univ, Coll Sci, Shenyang 110819, Peoples R China.;

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1. Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities [J] . DingZhai, LiweiAn, JinghaoLi, Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第5期

机译：具有不完善转移概率的离散时间分段齐次马尔可夫跳跃线性系统的镇定
2. Stability and Stabilization for Discrete-time Markovian Jump Stochastic Systems with Piecewise Homogeneous Transition Probabilities [J] . Zhou Meijiao, Fu Yanming International Journal of Control, Automation, and Systems . 2019,第9期

机译：具有分段均匀过渡概率的离散时间马尔可夫跳跃随机系统的稳定性和稳定性
3. Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time [J] . Wang Jimin, Ma Shuping, Zhang Chenghui Journal of the Franklin Institute . 2017,第5期

机译：具有平均停留时间的分段恒定转移概率的非线性离散时间奇异Markov跳跃系统的有限时间稳定
4. Robust fault detection for nonlinear discrete-time Markovian jump systems with partly unknown transition probabilities [C] . Jiangbin Shi, Yanyan Yin, Fei Liu World Congress on Intelligent Control and Automation . 2016

机译：转移概率部分未知的非线性离散时间马尔可夫跳跃系统的鲁棒故障检测
5. Detecting piecewise linear networks using reversible jump Markov Chain Monte Carlo. [D] . Apte, Akshay. 2010

机译：使用可逆跳跃马尔可夫链蒙特卡罗检测分段线性网络。
6. Markov Jump Linear Systems-Based Position Estimation for Lower Limb Exoskeletons [O] . Samuel L. Nogueira, Adriano A. G. Siqueira, Roberto S. Inoue, 2014

机译：基于Markov Jump线性系统的下肢外骨骼位置估计
7. On designing overlapping group mode-dependentH∞controllers of discrete-time Markovian jump linear systems with incomplete mode transition probabilities [O] . Xiaohua Ge, Qing-Long Han 2014

机译：在设计重叠群模式的上依赖性的离散时间Markovian跳转线性系统的重叠群模式 - 具有不完整模式的转换概率
8. Discrete-Time Markovian Jump Linear Systems [R] . Szajowski, K., de Koning, W. L. 1992

机译：离散时间马尔可夫跳跃线性系统

Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

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