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奇异摄动系统的二次稳定性和二次可镇定性 被引量：2

Quadratic Stability and Quadratic Stabilizability for Singularly Perturbed System
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摘要 讨论了连续奇异摄动系统的二次稳定性,利用线性矩阵不等式方法,推导了奇异摄动系统二次稳定性的充分条件,并给出了二次可镇定并可解的充分条件和二次可镇定的状态反馈控制器的一种迭代求法.利用MATLAB工具箱仿真验证了结果的正确性.并且和同阶次的正常系统算法进行了有效的比较,论证了奇异摄动方法解决stiff问题的有效性. Quadratic stability is proposed for singularly pe rt urbed continuous systems. Using the linear matrix inequality, a sufficient condi tion is derived for quadratic stability and another sufficient condition is give n for quadratic stabilizability and solvability of singularly perturbed systems. A feedback controller for quadratic stabilization is designed with an iterative algorithm. An example is worked out to illustrate the effectiveness of the meth od and the simulation results are given by the MATLAB tool box. The method is ef fective for stiff questions by comparing with that of regular systems.
作者 蔡晨晓 邹云 徐胜元
机构地区 南京理工大学自动化系
出处 《信息与控制》 CSCD 北大核心 2005年第3期344-349,共6页 Information and Control
基金 国家自然科学基金资助项目(60474078 60304001)
关键词 奇异摄动系统 二次稳定 二次可镇定 线性矩阵不等式(LMI) singularly perturbed system quadratic stability quad ratic stabilizability linear matrix inequality(LMI)
分类号 TP11 [自动化与计算机技术—控制理论与控制工程]
  • 相关文献

参考文献7

  • 1Barmish B R. Necessary and sufficient conditions for quadratic stability of an uncertain system [ J]. Journal of Optimal Theory and Application, 1985, 46(4) :399-408.
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  • 5蔡晨晓,邹云.奇异摄动系统的二次稳定[J].南京理工大学学报,2004,28(4):337-340. 被引量：2
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二级参考文献6

  • 1[1]Barmish B R.Necessary and sufficient conditions for quadratic stability of an uncertain system [J].Optimal Theory Application, 1985, 46 (4):399～408.
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共引文献1

同被引文献16

  • 1陈莉,程兆林.广义系统带干扰抑制的奇异LQ次优控制问题[C]//第五届全球智能控制与自动化大会.杭州:2004,1:572-576.
  • 2Li Chen,Zhaolin Cheng.Singular LQ Suboptimal Control Problem with Disturbance Rejection for Descriptor Systems[C]//Proceeding of the 2004 American Control Conference.Boston:2004:4595-4600.
  • 3Z Cheng,H Hong,J Zhang.The optimal regulation of generalized state-space systems with quadratic cost[J].Automatica,1988,24(5):697-710.
  • 4J Zhu,S Ma,Z Cheng.Singular LQ problem for descriptor systems[C]//Proc 38th IEEE Conf Decision Control.Arizona(USA):Phoenix,1999,4098-4099.
  • 5Harald K Wimmer.The Set of Positive Semidefinite Solutions of the Algebraic Riccati Equation of Discrete-Time Optimal Control[J].IEEE Transactions on Automatic Control,1996,41(5):660-671.
  • 6H Kwakernaak,R Sivan.Linear Optimal Control Systems[M].New York(USA):Wiley,1972.
  • 7Harald K Wimmer.Monotonicity and Maximality of Solutions of Discrete-Time Algebraic Riccati Equations[J].Journal of Mathematical Systems,Estimation and Control,1992,2(2):219-235.
  • 8钟宁帆,孙敏慧,邹云.奇异摄动系统的H_∞控制:基于奇异系统的方法[J].控制理论与应用,2007,24(5):701-706. 被引量：4
  • 9张柯,姜斌.基于故障诊断观测器的输出反馈容错控制设计[J].自动化学报,2010,36(2):274-281. 被引量：41
  • 10曹宁,张化光,罗艳红,冯德志,刘燕.一类非线性奇异摄动系统的近似最优控制[J].控制理论与应用,2011,28(5):688-692. 被引量：5

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信息与控制
2005年 第3期

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