Finite-Time H ∞ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

Abstract

This paper is concerned with the finite-time $H_{\infty }$ filtering problem for linear continuous time-varying systems with uncertain observations and ℒ ₂-norm bounded noise. The design of finite-time $H_{\infty }$ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time $H_{\infty }$ filtering problem is solved. A numerical example is given to illustrate the performance of the $H_{\infty }$ filter.