On the destabilizing effect of cross-coupling in decentralized adaptive control
type: Item
instance of: scholarly article
title: On the destabilizing effect of cross-coupling in decentralized adaptive control
zbMATH Open document ID: 0564.93047
DOI: 10.1016/0167-6911(85)90004-0
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The stability of square multivariable linear time-invariant (LTI) systems coupled with an adaptive controller for which the process cross-coupling terms have been neglected is studied in this paper. Our aim is to find conditions over the reference signals richness and the process transfer matrix frequency response such that, for sufficiently small adaptation rates, the stability of the adaptive system is insured. It is shown that if the adaptive system without interconnections is stable then stability of the overall system is preserved if either: (1) The frequency bands of the reference signals are non-overlapping. (2) When there is a spectrum overlap each output of the LTI system to input signals in this spectrum has an average energy where the contribution from its corresponding input is larger than the one due to the other inputs. Global results are obtained for a simple single-parameter adaptation scheme. The extension to general adaptive controllers is straightforward in a local context.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 3900639
zbMATH Keywords: square multivariable linear time-invariant systems
zbMATH Keywords: adaptive controller
zbMATH Keywords: cross-coupling
author: Romeo Ortega
author: Rafael Kelly
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90004-0
OpenAlex ID: W2039337395
cites work: Q5580482
cites work: A stability-instability boundary for disturbance-free slow adaptation with unmodeled dynamics
cites work: Q2981262
cites work: Q3857636
cites work: Decentralized indirect adaptive control of interconnected systems
description: scientific article; zbMATH DE number 3900639