Robust output feedback control of nonlinear singularly perturbed systems
type: Item
instance of: scholarly article
title: Robust output feedback control of nonlinear singularly perturbed systems
zbMATH Open document ID: 0939.93025
DOI: 10.1016/S0005-1098(99)00105-3
author: Panagiotis D. Christofides
published in: Automatica
publication date: 2000-07-05T00:00:00Z
review text: Nonlinear singularly perturbed systems with time-varying uncertain variables are considered. The system under consideration is: \[ \begin{aligned} \dot x & = f_1(x,\theta(t))+ Q_1(x,\theta(t))z+ g_1(x,\theta(t))u,\\ \varepsilon\dot z & = f_2(x,\theta(t))+ Q_2(x,\theta(t))z+ g_2(x,\theta(t))u,\tag{1}\\ y & = h(x),\end{aligned} \] where \(x\in \mathbb{R}^n\), \(z\in\mathbb{R}^p\) are the states, \(u\in\mathbb{R}\) denotes the manipulated input, \(\theta\in\mathbb{R}^q\) denotes the vector of the uncertain time-varying variables, \(y\in\mathbb{R}\) denotes the controlled output, \(\varepsilon\) is a small positive parameter, \(f_j(x,\theta(t))\), \(g_j(x,\theta(t))\), \(j= 1,2\) are sufficiently smooth vector functions, \(Q_j(x,\theta(t))\), \(j= 1,2\) are sufficiently smooth matrices and \(h(x)\) is a sufficiently smooth scalar function. It is assumed that the fast subsystem is asymptotically stable and the slow subsystem is input/output linearizable and possesses an input-to-state stable (ISS) inverse dynamics. For these systems, a robust output feedback controller is synthesized in order to ensure boundedness of the state and enforces robust asymptotic output tracking with attenuation of the effect of the uncertain variables on the output of the closed-loop system. The controller is constructed through combination of a high-gain observer with a robust state feedback controller synthesized via Lyapunov's direct method. The proposed controller enforces the aforementioned properties in the closed-loop system, for initial conditions, uncertainty and rate of change of uncertainty in arbitrarily large compact sets, provided that the singular perturbation parameter is sufficiently small and the observer gain is sufficiently large.
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 1389424
zbMATH Keywords: nonlinear singularly perturbed systems
zbMATH Keywords: input/output linearizable
zbMATH Keywords: high-gain observer
zbMATH Keywords: robust state feedback controller
reviewed by: Vasile Dragan
MaRDI profile type: Publication
cites work: Robust semi-global output tracking for nonlinear singularly perturbed systems
cites work: Singular perturbations and input-to-state stability
cites work: Feedback control of two-time-scale nonlinear systems
cites work: Control of Uncertain Nonlinear Systems
cites work: Robust servomechanism output feedback controllers for feedback linearizable systems
cites work: Stability analysis of nonlinear multiparameter singularly perturbed systems
cites work: Semiglobal stabilization of a class of nonlinear systems using output feedback
cites work: Q3791007
cites work: Asymptotic regulation of minimum phase nonlinear systems using output feedback
cites work: Smooth stabilization implies coprime factorization
cites work: Tools for Semiglobal Stabilization by Partial State and Output Feedback
full work available at URL: s0005-1098(99)00105-3
OpenAlex ID: W2092229598
Recommended article: Robustness of dynamic output feedback control for singular perturbation systems
Recommended article: Dynamic output feedback control of nonlinear singularly perturbed systems
Recommended article: Output feedback control for a class of singularly perturbed uncertain nonlinear systems
Recommended article: On output feedback control of singularly perturbed systems
Recommended article: Robust output regulation of singular nonlinear systems
Recommended article: Robust feedback control of singularly perturbed uncertain dynamical systems
Recommended article: Robust near-optimal output feedback control of non-linear systems
Recommended article: Q4732396
Recommended article: Q3501737
Recommended article: Feedback control of nonstandard singularly perturbed systems
description: scientific article; zbMATH DE number 1389424