Robust stability, adjoints and LQ control of scale delay systems

Author

Verriest, Erik I.

Author_Institution

Sch. of Electr. & Comput. Eng, Georgia Inst. of Technol., Atlanta, GA, USA

Volume

1

fYear

1999

fDate

6/21/1905 12:00:00 AM

Firstpage

209

Abstract

The Lyapunov-Krasovskii theory is used to derive sufficient conditions for robust stability (independent of delay) for a special class of functional differential systems with time variant delays. The existence of a triple of positive definite matrices satisfying a certain Riccati-like equation is shown to imply the robust stability. The connection between Hurwitz stability and Schur-Cohn stability of certain system matrices with this Riccati equation is presented. The approach readily yields stabilizability conditions under state feedback. The adjoint equations and optimal LQ control for such systems are derived. It is shown that the optimal regulator involves the feedback of a formal series of point delayed states. A sufficient condition for convergence of this series is given

Keywords

Riccati equations; convergence; delay systems; linear quadratic control; matrix algebra; robust control; series (mathematics); state feedback; Hurwitz stability; LQ control; Lyapunov-Krasovskii theory; Riccati-like equation; Schur-Cohn stability; adjoints; functional differential systems; optimal regulator; positive definite matrices; robust stability; scale delay systems; stabilizability conditions; sufficient conditions; time variant delays; Asymptotic stability; Control systems; Delay effects; Delay systems; Difference equations; Nonlinear equations; Optimal control; Riccati equations; Robust stability; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-5250-5

Type

conf

DOI

10.1109/CDC.1999.832776

Filename

832776