New approaches to robust minimum variance filter design

This paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete-time systems with parametric uncertainty residing in a polytope. Two efficient methods for robust Kalman filter design are introduced. The first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design. The second applies the new method of recursively solving a semidefinite program (SDP) subject to linear matrix inequalities (LMIs) constraints to obtain a robust finite horizon time-varying filter. The proposed design techniques are compared with other existing methods. It is shown, via two examples, that the results obtained by the new methods outperform all of the other designs.