Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions

2018/03/15 by Carsten W. Scherer, Scherer, Carsten W., Joost Veenman +1 · 2 citations
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #Engineering and Materials Science Studies #math.OC

paper · pdf · doi:10.48550/arxiv.1803.05804

arxiv created 2018/03/15 · arxiv updated 2018/03/16

Abstract

In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections based on the notion of finite-horizon integral quadratic constraints with a terminal cost. As the main benefit, this opens up opportunities for guaranteeing constraints on the transient responses of trajectories in feedback loops within absolute stability theory. For parametric robustness, we show how to generate tight robustly invariant ellipsoids on the basis of a classical frequency-domain stability test, with illustrations by a numerical example.

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