Robust H∞ filtering for discrete time-varying uncertain systems with a known deterministic input

Abstract

In this paper, a new discrete-time dynamic game where two players seek to reinforce and suppress the output of a system under the influence of a known deterministic input is considered. A necessary and sufficient condition for the existence of a saddle-point solution to this game is derived in terms of a discrete-time Riccati difference equation. The result of the game is used to solve the robust H∞ filtering problem for discrete time-varying systems subject to a known deterministic input and norm-bounded parameter uncertainties occurring in both the state and the output matrices of the state-space model. There is no restriction on the form of the filter. This allows the effect of the known input on the estimation error due to system uncertainties to be optimally reduced without any prior assumption on the filter structure.