一类广义混杂系统的随机稳定性及稳定化

doi:10.3969/j.issn.1001-2400.2010.05.016

J4 ›› 2010, Vol. 37 ›› Issue (5): 866-871.doi: 10.3969/j.issn.1001-2400.2010.05.016

一类广义混杂系统的随机稳定性及稳定化

杨莹^1,2;李俊民¹;陈国培²

(1. 西安电子科技大学理学院，陕西西安 710071；
2. 惠州学院数学系，广东惠州 516007)

收稿日期:2010-01-19 出版日期:2010-10-20 发布日期:2010-10-11
通讯作者: 杨莹
作者简介:杨莹(1979-)，女，西安电子科技大学博士研究生，E-mail: yy1502@sina.com．
基金资助:
国家自然科学基金资助项目(60374015,60974139)

Stochastic stability and stabilization for a class of singular hybrid systems

YANG Ying^1,2;LI Jun-min¹;CHEN Guo-pei²

(1. School of Science, Xidian Univ., Xi'an 710071， China;
2. Dept. of Mathematics, Huizhou Univ., Huizhou 516007， China)

Received:2010-01-19 Online:2010-10-20 Published:2010-10-11
Contact: YANG Ying

摘要/Abstract

摘要：

针对切换序列为齐次有限状态Markov链的离散广义混杂系统，采用多Lyapunov函数和随机广义Lyapunov函数相结合的方法，无需对广义系统作受限等价变换，得到了系统随机稳定的充要条件，该条件以耦合广义Lyapunov方程(Coupled Generalized Lyapunov Equation，缩写CGLEs)的形式给出，可化为严格线性矩阵不等式(SLMIs)来进行求解．然后，进一步对系统的稳定化问题进行了分析与设计，给出了状态反馈增益矩阵的求解方法．最后的数值算例说明了该方法的有效性．

关键词: 离散广义混杂系统, 耦合广义Lyapunov方程, 随机系统, 稳定性, 稳定化

Abstract:

Based on the method combining the techniques of the multiple Lyapunov function and stochastic generalized Lyapunov function, a necessary and sufficient condition is derived for discrete-time singular hybrid systems with the time-homogenous finite state Markov chain without using the restricted equivalent property of singular systems. The condition is given in terms of coupled generalized Lyapunov equations (CGLEs) such that the solution of the systems is stochastically stable. The equations can be solved by changing them into strict linear matrix inequalities (SLMIs). The result is extended to solve the stabilization problem and the design of a state-feedback controller. A numerical example shows the effectiveness of the proposed approach.

Key words: discrete-time singular hybrid systems, coupled generalized Lyapunov equations, stochastic systems, stability, stabilization

杨莹;李俊民;陈国培. 一类广义混杂系统的随机稳定性及稳定化[J]. J4, 2010, 37(5): 866-871.

YANG Ying;LI Jun-min;CHEN Guo-pei. Stochastic stability and stabilization for a class of singular hybrid systems[J]. J4, 2010, 37(5): 866-871.

参考文献

[1] Decarlo R A, Branicky M S, Pettersson S, et al. Perspective and Results on the Stability and Stabilizability of Hybrid Systems [J] . Proceedings of the IEEE, 2000, 88(7): 1069-1082.
[2] Liu B, Hill D J. Comparison Principle and Stability of Discrete-time Impulsive Hybrid Systems [J] . IEEE Trans on Circuits and Systems, 2009, 56(1): 233-245.
[3] Cai C, Teel A. Characterizations of Input-to-state Stability for Hybrid Systems [J] . Automatica, 2009, 58(1): 47-53.
[4] 陈国培, 李俊民, 杨莹. 一类不确定脉冲混合系统的非脆弱控制器设计[J] . 西安电子科技大学学报, 2008, 35(1): 65-70.
Chen Guopei, Li Junmin, Yang Ying. Design Methods for Non-fragile Controllers for a Class of Uncertain Impulsive Hybrid Syste-ms[J] . Journal of Xidian University, 2008, 35(1): 65-70.
[5] Ji Y, Chizeck H J. Controllability, Stability and Continuous-time Markovian Jump Linear Quadratic Control [J] . IEEE Trans on Automatic Control, 1990, 35(7): 777-788.
[6] Zhang L, Boukas E K. Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities [J] . Automatica, 2009, 45(2): 463-468.
[7] De Souza C E. Robust Stability and Stabilization of Uncertain Discrete-time Markovian Jump Linear Systems [J] . IEEE Trans on Automatic Control, 2006, 51(5): 836-841.
[8] Sathananthan S, Adetona O, Beane C, et al. Feedback Stabilization of Markov Jump Linear Systems with Time-Varying Delay [J] . Stochastic Analysis and Applications, 2008, 26(3): 577-594.
[9] Ishhara J Y, Terra M H. On the Lyapunov Theorem for Singular Systems [J] . IEEE Trans on Automatic Control, 2002, 47(11): 1926-1930.
[10] Masubuchi I, Kamitane Y, Ohara A, et al. H_∞ Control for Descriptor Systems: a Matrix Inequalities Approach [J] . Automatica, 1997, 33(4): 669-673.
[11] Xu S, Lam J. Robust Control and Filtering of Singular Systems [M] . Berlin: Springer, 2006.
[12] Boukas E K. On Robust Stability of Singular Systems with Random Abrupt Changes [J] . Nonlinear Analysis, 2005, 63(3), 301-310.
[13] Fu Yanming, Duan Guangren. Robust Guaranteed Cost Observer for Uncertain Descriptor time-delay Systems with Markovian Jumping Parameters [J] . Acta Automatica Sinica, 2005, 31(3): 149-153.
[14] Boyd S, Ghaoui E I, Feron E, et al. Linear Matrix Inequalities in System and Control Theory [M] . Philadelphia: SIAM, 1994.
[15] Xia Y Q, Zhang J H, Boukas E K. Control for Discrete Singular Hybrid Systems [J] . Automatica, 2008, 44(10): 2635-2641.
[16] Xu S Y, Lam J. Robust Stability and Stabilization of Discrete Singular Systems: an Equivalent Characterization [J] . IEEE Trans on Automatic Control, 2004, 49(4): 568-574.
[17] Xie L. Output Feedback H_∞ Control of Systems with Parameter Uncertainty [J] . Int J Control, 1996(63): 741-750.

一类广义混杂系统的随机稳定性及稳定化

Stochastic stability and stabilization for a class of singular hybrid systems

PDF (PC)

赞

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	张玉强;葛德彪. 一种高稳定的复杂色散介质分析FDTD方法[J]. 西安电子科技大学学报, 2018, 45(4): 118-122+173.
[2]	刘长江;万坚;韩杰思;魏强. 利用包长特征的浏览器被动识别方法[J]. 西安电子科技大学学报, 2017, 44(6): 144-149.
[3]	王辉;宋燕平;马小飞. 非对称环形天线型面稳定性的参数匹配设计方法[J]. 西安电子科技大学学报, 2017, 44(3): 114-119.
[4]	韦慧玲;仇原鹰;盛英. 高速绳牵引摄像机器人的运动稳定控制[J]. 西安电子科技大学学报, 2016, 43(5): 63-69+104.
[5]	刘鹏;仇原鹰. 绳牵引摄像机器人的力位混合稳定性评价方法[J]. J4, 2016, 43(1): 87-93.
[6]	刘家辰;苗启广;宋建锋;曹莹 . 使用聚类稳定性分析方法增强单类学习算法 [J]. J4, 2015, 42(2): 58-64+121.
[7]	陈佳;方洋旺;楼顺天. 非线性随机跳变摄动系统的鲁棒H_∞全阶观测器[J]. J4, 2013, 40(3): 57-65.
[8]	李素兰. 考虑闭环稳定性的曲柄滑块机构集成设计[J]. J4, 2013, 40(2): 43-47.
[9]	袁冰1;2;来新泉2;贾新章1;叶强2;王红义2. 片内频率补偿实现电流模DC-DC高稳定性[J]. J4, 2008, 35(4): 685-690.
[10]	曹寒梅1;杨银堂1;蔡伟2;陆铁军2;王宗民2. 一种结构简单的曲率补偿CMOS带隙基准源 [J]. J4, 2008, 35(4): 620-623.
[11]	陈龙;陈建军;马娟;张雪峰. 随机参数结构振动控制的特征值分析 [J]. J4, 2008, 35(2): 324-329.
[12]	肖剑1;莫良华2; 刘元成2;张福甲1. 一种新型内置频率补偿的LDO调整器设计 [J]. J4, 2007, 34(7): 181-184.
[13]	赵俊;孙小菡. 异步光分组交换型高性能计算机系统架构及性能分析 [J]. J4, 2007, 34(7): 193-196.
[14]	张喜民(1;2);周利华(2);车向泉(2). 基于时滞系统模型的网络控制系统稳定条件[J]. J4, 2006, 33(3): 404-407.
[15]	张海琴;于力;马华;任春丽. 一个矩阵微分方程的全局指数稳定性分析[J]. J4, 2005, 32(6): 961-964.