Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays
Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays
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DOI：
10.1080/00207170701261986
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发表时间：
2008-06
影响因子：
2.1
通讯作者：
Zhan Shu;J. Lam
中科院分区：
文献类型：
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作者：
Zhan Shu;J. Lam
研究了一类具有离散和分布时滞的不确定广义系统的指数估计和镇定问题。利用线性矩阵不等式（LMI）技巧和一个新的Lyapunov-Krasovskii泛函，建立了一个不仅保证指数稳定性和可容许性，而且给出衰减率和衰减系数估计的充分条件.估计过程是通过求解一组线性矩阵不等式来实现的，这些线性矩阵不等式可以很容易地通过有效的算法来检查。在此条件下，代数子系统具有与微分子系统相同的衰减率。此外，状态反馈镇定控制器的设计，使闭环系统指数稳定和容许的衰减率的一个指定的下界。数值例子说明了理论结果的有效性。
This paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays. A sufficient condition, which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient, is established in terms of the linear matrix inequality (LMI) technique and a new Lyapunov–Krasovskii functional. The estimating procedure is implemented by solving a set of LMIs, which can be checked easily by effective algorithms. Under the proposed condition, the algebraic subsystems possess the same decay rate as the differential ones. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.