Technical communique: Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach
Technical communique: Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach
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DOI：
10.1016/j.automatica.2010.02.022
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发表时间：
2010-05
期刊：
影响因子：
6.4
通讯作者：
Z. Zuo;D. Ho;Yijing Wang
中科院分区：
文献类型：
--
作者：
Z. Zuo;D. Ho;Yijing Wang
本文研究同时具有多面体参数不确定性和有界峰值输入的时滞系统的可达集估计问题。极大Lyapunov-Krasovskii泛函被构造为一族Lyapunov-Krasovskii泛函的点态极大值。每个泛函对应于不确定多面体的一个顶点。给出了确定可达集的若干准则。与传统的基于公共Lyapunov泛函的方法相比，该方法具有很大的优势。通过引入修正的积分不等式，放宽了对时滞导数小于1的限制。此外，当多面体的顶点数较少时，所得到的结果所需的计算量较小。文中给出了两个算例来说明理论结果。
This paper deals with the problem of reachable set estimation for time delay systems subject to both polytopic parameter uncertainties and bounded peak inputs. The maximal Lyapunov–Krasovskii functional is constructed as the pointwise maximum of a family of Lyapunov–Krasovskii functionals. Each functional corresponds to a vertex of uncertain polytope. Some criteria bounding the reachable set are derived. This approach shows great advantages over the traditional methods based on the common Lyapunov functionals. By introducing a modified integral inequality, the limitation imposed on the derivative of time delay being less than one is relaxed. Furthermore, the obtained results involve less computational burden when the number of vertices of the polytope is small. Two examples are given to illustrate the theoretical results.