Title:
Control of Slowly-Varying Linear Systems
Control of Slowly-Varying Linear Systems
Author(s)
Kamen, Edward W.
Khargonekar, Pramod P.
Tannenbaum, Allen R.
Khargonekar, Pramod P.
Tannenbaum, Allen R.
Advisor(s)
Editor(s)
Collections
Supplementary to
Permanent Link
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.
Sponsor
Date Issued
1989-12
Extent
Resource Type
Text
Resource Subtype
Article