Reduced-order H∞ filtering for singular systems

This paper solves the problem of reduced-order H-infinity filtering for singular systems. The purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular, impulse-free (or causal), stable, and satisfies a prescribed H-infinity performance level. One major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems. These conditions are characterized in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint. Moreover, an explicit parametrization of all desired reduced-order filters is presented when these inequalities are feasible. In particular, when a static or zeroth-order H-infinity filter is desired, it is shown that the H-infinity filtering problem reduces to a convex LMI problem. All these results are expressed in terms of the original system matrices without decomposition, which makes the design procedure simple and directly. Last but not least, the results have generalized previous works on H-infinity filtering for state-space systems. An illustrative example is given to demonstrate the effectiveness of the proposed approach. (c) 2006 Elsevier B.V All rights reserved.