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首页> 外文期刊>Automatic Control, IEEE Transactions on >Reducing the Complexity of the Sum-of-Squares Test for Stability of Delayed Linear Systems
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Reducing the Complexity of the Sum-of-Squares Test for Stability of Delayed Linear Systems

机译：减少平方和检验的复杂度，以了解延迟线性系统的稳定性

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摘要

This technical note considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this technical note considers systems with a large state-space but where delays affect only certain parts of the system. This yields a coefficient matrix of the delayed state with low rank—a common scenario in practice. The technical note uses the general framework of coupled differential-difference equations with delays in feedback channels. This framework includes systems of both the neutral and retarded-type. The approach is based on recent results which introduced a new Lyapunov–Krasovskii structure which was shown to be necessary and sufficient for stability of this class of systems. This technical note shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.
机译：本技术说明考虑了降低与Sum-of-Squares方法相关的时滞系统稳定性分析的计算复杂性的问题。具体而言，本技术说明考虑的是状态空间较大但延迟仅影响系统某些部分的系统。这产生了具有低秩的延迟状态的系数矩阵，这是实践中的常见情况。该技术说明使用耦合差分方程的一般框架，其中反馈通道存在延迟。该框架包括中性和迟滞型系统。该方法基于最近的结果，该结果引入了新的Lyapunov–Krasovskii结构，该结构被证明对于此类系统的稳定性是必要和充分的。本技术说明显示了如何利用新功能的结构可以显着提高计算复杂性。数值示例说明了这种改进。

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