Finite-time stabilization and   $H_\infty$ control of nonlinear delay systems via output feedback

Ta T.H. Trang; Vu N. Phat; Adly Samir

doi:10.3934/jimo.2016.12.303

Article Contents

2016, Volume 12, Issue 1: 303-315. Doi: 10.3934/jimo.2016.12.303

This issue Previous Article Subgradient-based neural network for nonconvex optimization problems in support vector machines with indefinite kernels Next Article An alternating direction method for solving a class of inverse semi-definite quadratic programming problems

Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback

1.
Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi 10307
2.
Université de Limoges, Laboratoire XLIM, 123, avenue Albert Thomas, 87060 Limoges CEDEX

Received: November 2014

Revised: January 2015

Published: January 2016

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Abstract

This paper studies the robust finite-time $H_\infty$ control for a class of nonlinear systems with time-varying delay and disturbances via output feedback. Based on the Lyapunov functional method and a generalized Jensen integral inequality, novel delay-dependent conditions for the existence of output feedback controllers are established in terms of linear matrix inequalities (LMIs). The proposed conditions allow us to design the output feedback controllers which robustly stabilize the closed-loop system in the finite-time sense. An application to $H_\infty$ control of uncertain linear systems with interval time-varying delay is also given. A numerical example is given to illustrate the efficiency of the proposed method.

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Mathematics Subject Classification: Primary: 93D20, 34D20; Secondary: 37C75.

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