New stability and stabilization conditions for systems with time-delay

Authors:
Yuanqing Xia;G. P. Liu;P. Shi;D. Rees;E. J. C. Thomas
Affiliations:
Department of Automatic Control, Beijing Institute of Technology, Beijing 100081, China,Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom,CSIS Lab, Institute of Automation, Chinese Academy of Sciences, China;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom
Venue:
International Journal of Systems Science
Year:
2007

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Abstract

In this article, the problems of stability and stabilization for systems with both constant and time-varying delays have been considered. By the so-called lifting method, time-delay systems are transformed into delay-free systems such that simple necessary and sufficient conditions have been developed for the stability analysis of systems with constant delays. For systems with time-varying delays, they have been converted to a switched system so that the existing results can be applied to analyze the problems of stability and stabilization. Linear matrix inequality (LMI) approach has been employed to the state feedback control design. Numerical examples are given to show the effectiveness of the proposed technique.