Inversion method in the discrete-time nonlinear control systems synthesis problems
type: Item
instance of: scholarly article
title: Inversion method in the discrete-time nonlinear control systems synthesis problems
zbMATH Open document ID: 0822.93001
DOI: 10.1007/3-540-19966-7
published in: Lecture Notes in Control and Information Sciences
publication date: 1995-06-28T00:00:00Z
review text: Discrete-time nonlinear control systems described by the equations \[ \begin{cases} x(t+ 1)= f(x(t), u(t), w(t)),\;x(t_ 0)= x_ 0,\;t= 0,1,2,\dots\\ y(t)= h(x(t), u(t))\end{cases}\tag{1} \] are considered, where \(x\in X\subset \mathbb{R}^ n\), \(u\in U\subset \mathbb{R}^ m\), \(w\in W\subset \mathbb{R}^ r\), \(y\in Y\subset \mathbb{R}^ p\) denote the state, the control, the disturbance and the output, respectively, \(f: X\times U\times W\to X\) and \(h: X\times U\to Y\) are smooth mappings. It is assumed that the whole state vector \(x\) can be measured. The structure and dynamic properties of (1) are changed by state or dynamic state feedbacks. A systematic approach based on system inversion is developed. The book consists of two parts. In the first part, special subsets of right invertible systems, the so-called \((d_ 1,\dots, d_ p)\)-forward time-shift right invertible systems are considered. In the second part, the generalized notion of the forward time-shift right invertibility is introduced. The inversion method is applied to the solution of the model matching problem, the disturbance decoupling problem and input-output decoupling problem. The input-output linearization problem via static and dynamic state feedback is considered. At the end of each chapter bibliographical notes are given. At the end of the book some open problems are discussed. The basic ideas are also applicable to continuous-time nonlinear systems, implicit systems, 2-D systems and distributed parameter systems.
reviewed by: Tadeusz Kaczorek
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 93A99
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 768075
zbMATH Keywords: discrete-time nonlinear
zbMATH Keywords: feedbacks
zbMATH Keywords: invertible systems
zbMATH Keywords: inversion method
zbMATH Keywords: model matching
zbMATH Keywords: disturbance decoupling
zbMATH Keywords: input-output decoupling
zbMATH Keywords: input- output linearization
author: Ülle Kotta
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/3-540-19966-7
OpenAlex ID: W406365488
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description: scientific article; zbMATH DE number 768075