New H_∞ FIR smoother for linear discrete-time state-space models

This letter propose a new H_∞ smoother (HIS) with a finite impulse response (FIR) structure for discrete-time state-space models. This smoother is called an H_∞ FIR smoother (HIFS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance. Among smoothers with these requirements, we choose the HIFS to optimize H_∞ performance criterion. The HIFS is obtained by solving the linear matrix inequality (LMI) problem with a parametrization of a linear equality constraint. It is shown through simulation that the proposed HIFS is more robust against uncertainties and faster in convergence than the conventional HIS.