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New results on stability and stabilisation of systems with interval time-varying delay

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4 Author(s)
J. Zhang ; Department of Automatic Control, Beijing Institute of Technology, Beijing 100081, People's Republic of China ; Y. Xia ; P. Shi ; M. S. Mahmoud

This study is concerned with the stability and stabilisation for systems with interval time-varying delay. First, by appropriately choosing Lyapunov functional and using Finsler's lemma, a new delay-dependent stability criteria involving the minimum and maximum delay bounds is obtained. Second, new results for delay-dependent stabilisation of systems with interval time-varying delay are provided on the basis of a linear matrix inequality (LMI) framework. Both state- and observer-based output feedback controllers are designed. Differing existing design approach of observer-based controller, a single-step approach is proposed to overcome the drawback of the two-step LMI approach often encountered in the literature, and the conditions are also delay dependent. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Published in:

IET Control Theory & Applications  (Volume:5 ,  Issue: 3 )