NDLI: Asymptotic Stabilization of Single-Input Linear Systems Having Unknown but Bounded Parameters

Content Provider	IEEE Xplore Digital Library
Author	Wei, Kehui
Copyright Year	1992
Description	Author affiliation: Concurrent Control Engineering Group, Institute for Flight Systems Dynamics, German Aerospace Research Establishment (DLR), D-8031, Oberpfaffenhofen, F. R. Germany (Wei, Kehui)
Abstract	This paper investigates the stabilization problem of single-input linear uncertain systems via constant state feedback control. The systems under consideration contain time-invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems. The criterion for the asymptotic stability of the closed-loop system (obtained when a state feedback control is applied) is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane. First, we show that to insure an interval system stabilizable, some entries of the system matrices must be sign invariant. More precisely, the number of the least-required sign-invariant entries in system matrices is equal to the system order. Then, we study the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign-invariant entries in proper locations. After dividing all standard systems into some subsets by the uncertainty locations, we then derive necessary and sufficient conditions under which every system in a subset is stabilizable, regardless of its parameter varying bounds. The conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a "generalized antisymmnetric stepwise configuration". The result is further generalized for unstandard systems via linear transformation.
Starting Page	1004
Ending Page	1008
File Size	393425
Page Count	5
File Format	PDF
ISBN	0780302109
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1992-06-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Linear systems Uncertain systems Robustness Uncertainty Control system synthesis Robust stability Control systems State feedback Sufficient conditions Stability criteria
Content Type	Text
Resource Type	Article

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