Reduced-Order $\mathcal {H}_{2}$ Filter Design for Discrete LRPs

Abstract

This chapter considers the reduced-order $\mathcal {H}_{2}$ filter design for discrete LRPs. Our aim is to design full- and reduced-order filters, which guarantee the filtering error process to be stable along the pass, and minimizes an upper bound for the $\mathcal {H}_{2}$ norm of its transfer function. Two sharply different approaches are developed to solve the reduced-order filtering problem. One is the convex linearization approach, which casts the reduced-order filtering into a convex optimization problem, and the other is the projection approach, which casts the reduced-order filtering into a sequential minimization problem subject to LMI constraints by employing the CCL algorithm. Solvability conditions are established for the desired full- and reduced-order H2 filters, respectively.