p主导系统的耗散性定理
A dissipativity theorem for p-dominant systems
AI总结：
本文在广义框架下重新审视线性二次理论的耗散性定理，探讨了二次存储在p维子空间中负定，在互补子空间中正定的性质，提出了一种用于分析低维吸引子互联系统的新型方法。
摘要：
我们重新审视线性二次理论的经典耗散性定理，将其推广到一个框架中，其中二次存储在p维子空间中为负定，在互补子空间中为正定。经典理论假设p=0，提供了一种用于稳定性分析的互联理论，即收敛到零维吸引子。广义理论被证明提供了一种用于p主导性分析的互联理论，即收敛到p维主导子空间。反过来，这一性质是非线性系统广义收缩性质的微分特征。所提出的推广为分析具有低维吸引子的互联系统开辟了新的途径。
英文摘要：
We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The classical theory assumes p = 0 and provides an inter- connection theory for stability analysis, i.e. convergence to a zero dimensional attractor. The generalized theory is shown to provide an interconnection theory for p-dominance analysis, i.e. convergence to a p-dimensional dominant subspace. In turn, this property is the differential characterization of a generalized contraction property for nonlinear systems. The proposed generalization opens a novel avenue for the analysis of interconnected systems with low-dimensional attractors.
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