Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty
type: Item
instance of: scholarly article
title: Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty
zbMATH Open document ID: 1011.93094
DOI: 10.1016/S0005-1098(02)00194-2
author: X. G. Yan
author: Lihua Xie
published in: Automatica
publication date: 2003-02-13T00:00:00Z
review text: The large-scale interconnected system is \(\dot{x}_i=A_ix_i+f(x_i)+B_i[u_i+\Delta\Psi_i(x_i)]+ \sum_{j\neq i} H_{ij}(x_j)+\Delta H_i(x)\), \(y_i=C_i x_i\), \(i=1,\ldots,N\). The nonlinear functions \(f_i\) are continuous, \(\Delta\Psi_i(x_i)\) is the matched uncertainty, \(\sum_{j\neq i} H_{ij}(x_j)\) is the known interconnection, and \(\Delta H_i(x)\) includes all mismatched uncertainties. Under certain technical assumptions, among which some ``similarity'' of the subsystems \((A_i,B_i,C_i)\) is the most important one, a constructive proof is given of a sufficient condition for the existence of a continuous reduced-order controller stabilizing the system. Estimates for the stability regions are included. No structural information on uncertainties in subsystems or interconnections is required, except that they can be bounded by known functions of states and inputs. Good robustness is obtained because known and uncertain interconnections are treated separately.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93A15
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1868225
zbMATH Keywords: reduced order control
zbMATH Keywords: nonlinear interconnected system
zbMATH Keywords: similarity
zbMATH Keywords: control feedback
zbMATH Keywords: stabilization
zbMATH Keywords: large-scale system
zbMATH Keywords: mismatched uncertainties
zbMATH Keywords: stability regions
MaRDI profile type: Publication
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full work available at URL: s0005-1098(02)00194-2
OpenAlex ID: W2019041634
description: scientific article; zbMATH DE number 1868225