New conditions for the exponential stability of evolution equations

Author

Hong, Keum-Shik ; Wu, Jinn W.

Author_Institution

Dept. of Mech. Design Eng., Pusan Nat. Univ., South Korea

fYear

1992

fDate

1992

Firstpage

363

Abstract

New conditions for the exponential stability of a linear finite-dimensional system as well as a class of infinite-dimensional systems described by parabolic partial differential equations are derived. It is shown for finite-dimensional systems that the frozen time analysis is justifiable for the systems that satisfy the Holder-type continuity, which is a broader class than the class of slowly varying systems. For parabolic systems, the restrictive condition, such as the existence of A(∞), has ben removed. The proofs are carried out using the semigroup theory and the variation of constant formulas, and specific bounds for constants such as K and L are given

Keywords

adaptive control; control system analysis; distributed parameter systems; feedback; linear systems; partial differential equations; stability; stability criteria; time-varying systems; Holder-type continuity; adaptive control; distributed parameter systems; evolution equations; exponential stability; frozen time analysis; infinite-dimensional systems; linear finite-dimensional system; parabolic partial differential equations; parabolic systems; restrictive condition; semigroup theory; time-varying systems; Adaptive control; Adaptive systems; Design engineering; Eigenvalues and eigenfunctions; Hilbert space; Partial differential equations; Programmable control; Stability; Stability analysis; Time varying systems; Tracking loops;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1992., Proceedings of the 31st IEEE Conference on

Conference_Location

Tucson, AZ

Print_ISBN

0-7803-0872-7

Type

conf

DOI

10.1109/CDC.1992.371715

Filename

371715