H∞H∞ fixed-lag smoothing for linear discrete time-varying systems with uncertain observations

This paper deals with the problem of H∞H∞ fixed-lag smoothing for linear discrete time-varying systems with uncertain observations and l2l2-norm bounded noise. First, the design of H∞H∞ smoother is equivalent to the problem that a certain indefinite quadratic form with respect to a new state-space constraints has a minimum and the smoother is such that the minimum is positive. Then, by introducing a Krein space stochastic system and applying re-organized innovation analysis approach, the minimum of indefinite quadratic form and its existence condition are derived. Finally, through analyzing the existence condition of the minimum and guaranteeing the positivity of the minimum, a sufficient and necessary condition for the existence of an H∞H∞ smoother is proposed and the smoother is obtained in terms of two standard Riccati difference equations. A numerical example is given to show the effectiveness of the proposed method.