On performance limitation factors in the h∞ preview problems

This paper studies the limiting factors on H^infin performance achievable in the fixed-lag smoothing problem, in both continuous and discrete time. It shows that geometric performance bounds are inherited from the fixed-interval (L^infin) problem, whereas analytic constraints, caused by unstable modes of the measurement channel pseudo-inverse, are affected by the preview interval. Thus, the fixed-lag problem can be 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.