Some properties and stability results for sector-bounded LTI systems

Author

Gupta, Sandeep ; Joshi, Suresh M.

Volume

3

fYear

1994

Firstpage

2973

Abstract

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector [a, b] in terms of linear matrix inequalities in its state-space realization matrices, which represent a generalization of similar conditions for bounded ℋ_∞-norm systems. Further, a weaker definition of LTI systems strictly inside sector [a,b] is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems

Keywords

Lyapunov methods; closed loop systems; feedback; interconnected systems; linear systems; matrix algebra; stability; state-space methods; Lyapunov function; bounded H_∞-norm systems; closed-loop stability; linear matrix inequalities; linear time-invariant system; necessary and sufficient conditions; negative feedback interconnection; sector conditions; sector-bounded LTI systems; state-space characterization; state-space realization matrices; Control systems; Linear matrix inequalities; Lyapunov method; NASA; Negative feedback; Postal services; Riccati equations; Robust stability; Sufficient conditions; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on

Conference_Location

Lake Buena Vista, FL

Print_ISBN

0-7803-1968-0

Type

conf

DOI

10.1109/CDC.1994.411339

Filename

411339