Abstract
AbstractThis paper is concerned with the design of observers for a linear system with time‐varying delay in the field of structural control. A class of sliding mode observers with state and input time‐varying delays is developed on the basis of the coordinate transformation and free‐weighting matrix methods. The exponential dynamic properties of the observers are introduced to improve the performance of the observer. The delay and delay‐rate dependent conditions formulated by linear matrix inequalities (LMIs) are proposed to obtain the gains of the observers. Then, the bisection method is proposed to obtain the maximum exponential decay rate and allowable time delay. Finally, a numerical example of a fourth‐order system is used to show the feasibility and efficiency of the proposed observer.
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