Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation
Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation
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DOI：
10.1109/tac.2006.875017
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发表时间：
2006-05
影响因子：
6.8
通讯作者：
G. Lu;D. Ho
中科院分区：
文献类型：
--
作者：
G. Lu;D. Ho
本文考虑具有非线性摄动的连续时间广义系统的广义二次稳定性问题。摄动是时间和系统状态的函数，并且满足Lipschitz约束。本文首先给出了广义系统解存在唯一性的一个充分条件。然后利用S方法和矩阵不等式方法，给出了一个线性矩阵不等式形式的充要条件，并在此条件下得到了保证系统广义二次稳定的最大摄动界。也就是说，系统保持指数稳定，标称系统是规则的和无脉冲的。此外，具有摄动的非奇异系统的鲁棒稳定性可以作为特例得到。最后，通过数值算例说明了该方法对广义系统和非广义系统的有效性。
This note considers the generalized quadratic stability problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples.