Adaptive stabilization of not necessarily minimum phase plants
type: Item
instance of: scholarly article
title: Adaptive stabilization of not necessarily minimum phase plants
zbMATH Open document ID: 0622.93034
DOI: 10.1016/0167-6911(86)90041-1
published in: Systems \& Control Letters
publication date: 1986-01-01T00:00:00Z
review text: The plant is represented by the equations \[ (1)\quad \dot x=A_ 0x+b_ 0u+A_{12}\eta,\quad x\in {\mathbb{R}}^ n,\quad \eta \in {\mathbb{R}}^ n,\quad \mu {\dot \eta}=A_{22}\eta +\mu b_ 1\dot u,\quad y=c_ 0^ Tx,y,\quad u\in {\mathbb{R}}^ 1. \] Here \(\mu >0\) is a small parameter and the coefficients in (1) are unknown. Let \(W_ 0(S)=c^*_ 0(sI-A_ 0)^{-1}b_ 0=gn(s)d(s)^{-1}\) be the transfer function of the dominant part of (1),n(s),d(s) are monic and g is known; without loss of generality \(g>0\). The adaptive regulator is taken in the form (2) \(u=- Ky,K=\gamma y.\) Let n(s) be Hurwitz and deg d(s)\(=\deg n(s)+1\). There exist \(\mu^*>0\), \(0<\alpha <1/2\), \(c_ j>0\) and \(\bar K\) such that for each \(\mu \in [0,\mu^*]\) every solution of (1), (2) which starts from the set \({\mathcal D}(\mu)=\{x,\eta,K:| x| +| K-\bar K| <c_ 1\mu^{- \alpha}\), \(| \eta | <c_ 2\mu^{-\alpha -1/2}\}\) is bounded and \(| x(t)| +| \eta (t)| \to 0\), \(K(t)\to K_{\infty}\) as \(t\to \infty\).
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 4010326
zbMATH Keywords: non-minimum phase plants
zbMATH Keywords: region of attraction
zbMATH Keywords: adaptive regulator
author: Petros A. Ioannou
reviewed by: V. A. Yakubovich
MaRDI profile type: Publication
full work available at URL: 0167-6911(86)90041-1
OpenAlex ID: W2150940718
cites work: Q3342304
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description: scientific article; zbMATH DE number 4010326