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Improved stability and stabilization approach to linear interconnected time-delay systems

机译：线性互连时滞系统的改进的稳定性和稳定化方法

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摘要

In this paper, we investigate the problems of delay-dependent analysis and state-feedback synthesis for a class of linear continuous-time interconnected systems with time-varying delays. An augmented Lyapunov functional is properly constructed for the individual subsystems and an improved free-weighting method is deployed to exhibit the delay-dependent dynamics. Delay-dependent stability analysis is then performed to develop linear matrix inequalities (LMIs)-based conditions under which the family of linear delay subsystems is asymptotically stable with a γ-level L_2-gain for the nominal model. Extension to systems with convex bounded parameter uncertainties in all system matrices is also provided. All the required numerical computations are performed on the subsystem level. By delay-dependent stabilization, we design a family of local state-feedback schemes to guarantee that the closed-loop subsystem enjoys the delay-dependent asymptotic stability with a prescribed γ-level L_2-gain. The developed results are tested on a representative example to illustrate the theoretical developments.
机译：在本文中，我们研究了一类具有时变时滞的线性连续时间互联系统的时滞相关分析和状态反馈综合问题。为各个子系统正确构建了增强的Lyapunov功能，并采用了一种改进的自由加权方法来展示依赖于延迟的动态特性。然后进行依赖于延迟的稳定性分析，以开发基于线性矩阵不等式（LMI）的条件，在该条件下，线性延迟子系统族在名义模型的γ级L_2增益下渐近稳定。还提供了对所有系统矩阵中具有凸有界参数不确定性的系统的扩展。所有必需的数值计算都在子系统级别上执行。通过依赖于延迟的稳定，我们设计了一系列局部状态反馈方案，以确保闭环子系统在规定的γ级L_2增益下具有依赖于延迟的渐近稳定性。在一个代表性的例子上测试了开发的结果，以说明理论上的发展。

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