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

This paper is concerned with the finite-time H∞ filtering problem for linear continuous timevarying systems with uncertain observations and L2-norm bounded noise. The design of finitetimeH∞ 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 statespace model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time H∞ filtering problem is solved. A numerical example is given to illustrate the performance of the H∞ filter.