DESIGN OF OPTIMAL REDUCED-ORDER FILTER FOR UNSTABLE DISCRETE-TIME-SYSTEMS

The paper is concerned with H-2 optimal reduced-order filtering for a linear discrete time: signal model, The signal. model is allowed to be unstable. The objective is: to obtain a reduced- order filter that no t only gives rise to a: stable filtering error transfer function but a lso minimises the HT norm. The authors first derive a parameterisation of a set of filters of fixed order which lead to stable filtering err or transfer functions. Such a parameterisation is given in terms of an arbitrary orthogonal projection matrix. As a consequence, the problem of minimising the Hz norm of the filtering error transfer function ov er the set: of; reduced-order filters is formulated as an equivalent u nconstrained parametric optimisation, problem over a compact manifold. Two gradient-based: algorithms are then, proposed to compute an. opti mal reduced-order filter. The good properties of the algorithms, inclu ding: the convergence property, are established theoretically as well as demonstrated numerically with an example..