Guaranteed cost and H∞ filtering for time delay systems

In this paper, we consider the guaranteed cost filtering and H_∞ filtering design methods for linear time delay systems in continuous-time and discrete-time, respectively. The main purpose is to design stable filters which minimize the guaranteed cost in guaranteed cost filter and H_∞ performance measure in H_∞ filter. In guaranteed cost filtering, the sufficient conditions for the existence of filters, the guaranteed cost filter design method, and the upper bound of the guaranteed cost axe proposed. Also, the sufficient conditions for the existence of H_∞ filters, the H_∞ filter design method, and the upper bound of H_∞ norm are presented in H_∞ filtering. Since the proposed sufficient conditions are LMI(linear matrix inequality) forms in terms of all finding variables, all solutions can be obtained simultaneously. Moreover, we present optimization problems in order to get the optimal guaranteed cost filters and H_∞ filters in continuous-time and discrete-time case, respectively