Differential stability and robust control of nonlinear systems
type: Item
instance of: scholarly article
title: Differential stability and robust control of nonlinear systems
zbMATH Open document ID: 0808.93017
DOI: 10.1007/BF01211498
author: Tryphon T. Georgiou
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1994-08-14T00:00:00Z
review text: This paper deals with the problem of the robust input-output stabilization of nonlinear systems. The key machinery is provided by an extension of the gap metric, referred to as the differentiable gap between nonlinear dynamical systems which possess a differentiable graph, i.e. that admit an approximation by a linear system about any input- output bounded trajectory. The differentiable gap is a pseudo-metric in the sense that two different dynamical systems may have zero differentiable gap. However, it is still well suited for a quantitative description of the robustness of stability in a feedback interconnection. In fact, system perturbations are measured with the differentiable gap. The robustness of stability of a stable feedback interconnection is characterized in terms of a minimal opening between two nonlinear manifolds (system and controller graphs).
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 618215
zbMATH Keywords: robust input-output stabilization of nonlinear systems
zbMATH Keywords: gap metric
reviewed by: Maria D. Di Benedetto
MaRDI profile type: Publication
cites work: Q4746527
cites work: A quantitative condition for the well-posedness of interconnected dynamical systems
cites work: Some metrics on the subspaces qf a Banach space
cites work: The parallel projection operators of a nonlinear feedback system
cites work: Optimal robustness in the gap metric
cites work: Q4273645
cites work: Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty
cites work: Estimation of iterated matrices, with application to the von Neumann condition
cites work: Q5526485
cites work: Stability of control systems and graphs of linear systems
cites work: Feedback stability under simultaneous gap metric uncertainties in plant and controller
cites work: Q3346137
cites work: A pointwise criterion for controller robustness
cites work: Coprime fractional representations and stability of non-linear feedback systems
cites work: On the well-posedness of large-scale interconnected systems
cites work: The graph metric for unstable plants and robustness estimates for feedback stability
cites work: Robust controllers for uncertain linear multivariable systems
cites work: Frequency domain uncertainty and the graph topology
cites work: Q5656654
cites work: Sufficient conditions for robust BIBO stabilization: Given by the gap metric
description: scientific article; zbMATH DE number 618215