<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed <italic>α</italic>-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.</p></abstract>

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

Observer-based controller design of time-delay systems with an interval time-varying delay

Department of Mathematics and Informatics Thai Nguyen University of Sciences, Quyet Thang Ward, Thai Nguyen City 23000, Vietnam

Institute of Mathematics VAST, 18 Hoang Quoc Viet Road, Hanoi 10307, Vietnam

School of Engineering Deakin University, Geelong, VIC 3217, Australia

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an...

Observer-based controller design of time-delay systems with an interval time-varying delay

Published Online: Dec 28, 2012

Page range: 921 - 927

DOI: https://doi.org/10.2478/v10006-012-0068-8

This content is open access.