This article considers the problem of control synthesis via state feedback for linear time-delay systems with design specifications in finite frequency ranges. First, a finite frequency performance analysis condition for time-delay systems is presented. Then, a resulting state feedback control synthesis condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, the design procedure and the effectiveness of the proposed method are illustrated via a numerical design example.
This paper is concerned with the delay-dependent filtering problem for linear discrete-time multi-delay systems with small gain conditions in finite frequency ranges. A new multiplier method is developed to convert the resulting nonconvex filtering synthesis conditions to the ones based on linear matrix inequalities (LMIs). Thus, sufficient conditions for the existence of feasible filters are given in terms of solutions to a set of LMIs. For the entire frequency case, it is shown that the proposed result is less conservative than the relative existing results. Finally, the procedures and the advantages of the proposed approach in comparison with the existing ones in the entire frequency range are illustrated via numerical examples.
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