论文标题
凸的非线性系统的增量消散性分析 - 扩展版本
Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
论文作者
论文摘要
在实际应用中，非线性系统的有效计算稳定性和性能分析变得越来越重要。消散性可以共同表达稳定性和性能，但现有结果仅限于这些非线性系统平衡点周围的区域。根据系统轨迹的收敛性，增量框架消除了此限制。我们研究了在增量框架中非线性系统的稳定性和性能特征如何链接到耗散性，以及如何在此框架中理解$ \ MATHCAL {L} _2 $ gain概念以外的一般性能表征。本文通过二次存储和供应功能提供了基于矩阵不平等的凸面增量消散性分析。提出的耗散性分析将增量，差异和一般消散性的概念联系起来。我们表明，通过差异性，可以保证非线性系统的增量和一般消散性。这些结果还导致了$ \ Mathcal {l} _2 $ - gain的增量扩展，概括性$ \ Mathcal {h} _2 $ -norm，$ \ Mathcal {l} _ \ infty $ gain $ gain，以及非线性系统的被动率。
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to the regions around the equilibrium points of these nonlinear systems. The incremental framework, based on the convergence of the system trajectories, removes this limitation. We investigate how stability and performance characterizations of nonlinear systems in the incremental framework are linked to dissipativity, and how general performance characterization beyond the $\mathcal{L}_2$-gain concept can be understood in this framework. This paper presents a matrix inequalities-based convex incremental dissipativity analysis for nonlinear systems via quadratic storage and supply functions. The proposed dissipativity analysis links the notions of incremental, differential, and general dissipativity. We show that through differential dissipativity, incremental and general dissipativity of the nonlinear system can be guaranteed. These results also lead to the incremental extensions of the $\mathcal{L}_2$-gain, the generalized $\mathcal{H}_2$-norm, the $\mathcal{L}_\infty$-gain, and passivity of nonlinear systems.
