Control of Slowly-Varying Linear Systems

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Title: Control of Slowly-Varying Linear Systems
Author: Kamen, Edward W. ; Khargonekar, Pramod P. ; Tannenbaum, Allen R.
Abstract: State feedback control of slowly varying linear continuous-time and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This study centers on pointwise stabilizable systems. These are systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Re s=-γ<0 in the complex plane (or within a disk of radius ρ<1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix ar continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small. It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation.
Description: ©1989 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. DOI: 10.1109/9.40776
Type: Article
ISSN: 0018-9286
Citation: E. W. Kamen, P. P. Khargonekar, and A. Tannenbaum, "Control of Slowly-Varying Linear Systems" IEEE Transactions on Automatic Control, Vol. 34, No. 12, 1283-1285
Date: 1989-12
Contributor: University of Pittsburgh. Dept. of Electrical Engineering
University of Minnesota. Dept. of Electrical Engineering
University of Michigan. Dept. of Electrical Engineering and Computer Science
Publisher: Georgia Institute of Technology
Institute of Electrical and Electronics Engineers
Subject: Closed loop systems
Discrete time systems
Eigenvalues and eigenfunctions
Linear systems
Matrix algebra
Time-varying systems

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