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首页> 外文会议>ASME Dynamic Systems and Control Conference >DISCRETIZED LYAPUNOV-KRASOVSKII FUNCTIONAL FOR SYSTEMS WITH MULTIPLE DELAY CHANNELS
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DISCRETIZED LYAPUNOV-KRASOVSKII FUNCTIONAL FOR SYSTEMS WITH MULTIPLE DELAY CHANNELS

机译：可离散的Lyapunov-Krasovskii用于多个延迟通道的系统功能

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摘要

Many practical systems have a large number of state variables but only a few components have time delays. These delay components are often scalar or low dimensional, and involve single time delay in each component. A coupled differential-difference equation is well suited to formulate such systems. It is known that such a formulation is very general. Systems with multiple related or independent delays can be transformed into this standard form. Similar to regular time-delay systems, the existence of a quadratic Lyapunov-Krasovkii functional is necessary and sufficient for stability. This article discusses the discretization of such a quadratic Lyapunov-Krasovskii functional. Even for time-delay systems of retarded type, the formulation has significant advantage over the traditional formulation, as the size of the resulting linear matrix inequalities are drastically reduced for such systems. Indeed, the computational effort needed for checking stability of such a large system with a few low dimensional delays is quite reasonable.
机译：许多实用系统具有大量状态变量，但只有少数组件有时间延迟。这些延迟组件通常是标量或低维度，并且涉及每个组件中的单个时间延迟。耦合的差分差分方程非常适合于配制这种系统。众所周知，这种制剂非常一般。可以将具有多个相关或独立延迟的系统转换为此标准表格。类似于常规时间延迟系统，存在二次Lyapunov-Krasovkii功能的必要性并且足以稳定。本文讨论了这种二次Lyapunov-Krasovskii功能的离散化。即使对于延迟类型的时滞系统，该配方均对传统制剂具有显着的优势，因为这种系统的所得线性基质不等式的尺寸大大降低。实际上，用几个低维延迟检查这种大型系统的稳定性所需的计算工作是相当合理的。

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