Global Convergence of a Class of Discrete-Time Interconnected Pendulum-Like Systems
Global Convergence of a Class of Discrete-Time Interconnected Pendulum-Like Systems
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DOI：
10.1007/s10957-007-9172-6
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发表时间：
2007-05
影响因子：
1.9
通讯作者：
Ying Yang;Z. Duan;Lin Huang
中科院分区：
文献类型：
--
作者：
Ying Yang;Z. Duan;Lin Huang
研究了一类离散时间关联类混沌系统。利用线性矩阵不等式（LMI）的形式，建立了线性部分同时具有结构和非结构不确定性系统全局收敛的充分条件。在传统的大系统分散控制中，很少考虑关联项的影响。为了讨论非线性互连的影响，本文引入了描述互连结构的方阵。结果表明，通过设计适当的互联矩阵，可以实现整个互联系统的全局收敛。为了解决综合问题中出现的非线性矩阵不等式问题，提出了一种全局优化算法，可用于处理一类非线性矩阵不等式问题。最后通过算例验证了主要结果和算法的适用性和有效性。
This paper focuses on a class of discrete-time interconnected pendulum-like systems. Sufficient conditions for the global convergence of systems with both structured and unstructured uncertainties in its linear part are established in terms of linear matrix inequalities (LMIs). In the traditional decentralized control of large scale systems, the effects of interconnections were seldom studied. In this paper, a square matrix specifying the interconnecting structure is introduced in order to discuss the effects of nonlinear interconnections. It is shown that the global convergence of the whole interconnected system can be achieved by designing an appropriate interconnection matrix. In order to solve the nonlinear matrix inequalities (NMIs) arising in the synthesis problem, a global optimization algorithm is presented which can be used to handle a class of NMI problems. An illustrative example is given to demonstrate the applicability and validity of the main results and the presented algorithm.