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An Asymmetric Small-Gain Theorem for Construction of Lyapunov-Krasovskii Functionals of Nonlinear Time-Delay Systems with Static Components

机译：具有静态组件的非线性时滞系统的Lyapunov-Krasovskii功能的非对称小增益定理

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Existing small-gain theorems for stability and robustness analysis usually rely on the symmetry of dissipative properties of systems. The standard ISS small-gain theorem as well as the recently-developed iISS small-gain theorem also assume that components are characterized in a symmetric way with respect to the equilibrium. Dissipative properties of a system is usually asymmetric when the system is nonlinear. Formulating it into a symmetric dissipation sometimes causes fatal conservativeness. Consideration of time-delays are also practically important in analysis of interconnected systems. This paper focuses on the problem of verifying stability and robustness of nonlinear time-delay systems and develops a small-gain theorem making use of integral input-to-state stable dynamic components and static components characterized in a symmetric way with respect to the equilibrium. A Lyapunov-Krasovskii functional establishing robustness with respect to disturbances in the presence of time-delays is constructed, and its effectiveness is illustrated by a network flow control example.
机译：稳定性和稳健性分析的现有小增益定理通常依赖于系统的耗散特性的对称性。标准ISS小增益定理以及最近开发的IISS小增益定理还假设组件的特征在于相对于均衡的对称方式。当系统非线性时，系统的耗散性质通常是不对称的。将其制定为对称耗散有时会导致致命的保守性。在对互联系统的分析中，考虑时间延迟也很重要。本文重点介绍了验证非线性时滞系统的稳定性和稳健性的问题，并开发了利用整体输入到状态稳定动态分量和静态分量以对称的方式相对于均衡方式表征的静态分量。构造了Lyapunov-Krasovskii功能建立相对于存在时滞的干扰的鲁棒性，并且网络流量控制示例示出了其有效性。

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