The$H_infty$Fixed-Interval Smoothing Problem for Continuous Systems

The$H_infty$smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an$H_infty$criterion by means of an artificial discontinuity that splits the problem in term of$H_infty$forward and$H_infty$backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Secondly, a backward filter is developed taking into account the backward Markovian model. The third step consists of combining the two previous steps in order to compute the$H_infty$smoothed estimate. An example shows the efficiency of this proposed smoother.