We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic (Ψ,Π,Υ,Ω)-dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static (Q,S,R)-dissipativity, dissipativity with terminal costs, etc. Comparison with the input–output approach to feedback stability analysis based on integral quadratic constraints is also made.

中文翻译：

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通过动态电源速率的耗散率进行反馈稳定性分析


我们提出了非线性系统动态供给率的耗散率的一般概念。这通过静态供应率和各种二次形式的动态供应率扩展了经典耗散率。本文的主要结果涉及非线性反馈耗散系统的 Lyapunov 和渐近稳定性分析，这些系统的特点是相对于兼容动态供应速率的耗散不等式，但可能涉及不同且独立的辅助系统。重要的是，提供了保证反馈系统状态稳定性的耗散条件，而无需担心辅助系统状态的稳定性。主要结果还专门用于动态 （Ψ，Π，Υ，Ω） 耗散性描述的两个非线性系统互连的简单耦合测试，并显示可以恢复文献中的几个现有结果，包括小增益、无源指数、静态 （Q，S，R） 耗散性、与终端成本的耗散性等。还与基于积分二次约束的反馈稳定性分析的输入-输出方法进行了比较。