Stable fixed-lag smoothing of continuous time processes

Attempts to realize optimal fixed-lag smoothers for continuous-time processes have encountered two major difficulties: the presence of delay lines in the smoother, and the instability of most smoothers. This paper considers suboptimal smoothers which still outperform filters and have performance very close to the optimum. Design procedures are exhibited for smoothers that are both finite-dimensional and asymptotically stable, with the procedures depending on the delay line being approximated by a finite-dimensional dynamical system.