New quasi-deadbeat FIR smoother for discrete-time state-space signal models: An LMI approach

In this letter, we propose a new H₂ smoother (H2Š) with a finite impulse response (FIR) structure for discrete-time state-space signal models. This smoother is called an H₂ FIR smoother (H2FS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance to design H2FS that is optimal in the sense of H₂ performance criterion. It is shown that H2FS design problem can be converted into the convex programming problem written in terms of a linear matrix inequality (LMI) with a linear equality constraint. Simulation study illustrates that the proposed H2FS is more robust against uncertainties and faster in convergence than the conventional H2S.