A Less Conservative LMI Condition for Stability of Discrete-Time Systems With Slope-Restricted Nonlinearities

Author

Ahmad, N. Syazreen ; Carrasco, J. ; Heath, W.P.

Author_Institution

Sch. of Electr. & Electron. Eng., Univ. Sains Malaysia, Nibong Tebal, Malaysia

Volume

60

Issue

6

fYear

2015

fDate

42156

Firstpage

1692

Lastpage

1697

Abstract

Many conditions have been found for the absolute stability of discrete-time Lur´e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames-Falb multipliers. Both conditions are related to the Jury-Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.

Keywords

absolute stability; control nonlinearities; convex programming; discrete time systems; linear matrix inequalities; search problems; IQCs; Jury-Lee criterion; LMI; Lyapunov theory; absolute stability; convex searches; discrete-time Lur´e systems; discrete-time systems; integral quadratic constraints; noncausal Zames-Falb multipliers; slope-restricted nonlinearities; Asymptotic stability; Frequency-domain analysis; Lyapunov methods; MIMO; Numerical stability; Stability criteria; Convex LMI; Lyapunov stability; discrete-time; multiplier theory;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2361398

Filename

6915687