On Geometric and Analytic Constraints in the ${H}^{{\infty} }$ Fixed-Lag Smoothing

Abstract

Limiting factors on achievable performance in the continuous- and discrete-time fixed-lag smoothing problems are shown to include geometric constraints, inherited from the fixed-interval (Linfin) problem, and analytic constraints, affected by the preview interval. Thus, the fixed-lag problem is viewed as a constrained version of its fixed-interval counterpart. The analysis sheds light on the dependence of achievable performance on the preview length and, in particular, on the generic presence of performance saturation at a finite preview interval.