H∞ norm principle in residual filter design for discrete-time linear positive systems

New method of residual filter synthesis for discrete-time linear strictly positive systems is developed in this paper. Introducing constraints of positive system parameter structure in the set of linear matrix inequalities and completing it with the inequality guaranteing asymptotic stability of the discrete-time positive linear observer structure, the formulation provides a generalized solution by which the observers and residual filters can be designed for positive and strictly positive systems. Capabilities of the proposed design conditions are demonstrated using numerical illustrative examples.