Algebraic LTI filter synthesis for simultaneously making a convex combination of discrete-time plants SPR

Given a segment of discrete-time plants that are not strictly positive real (SPR), we give a synthesis procedure that obtains a rational, causal and minimum-phase filter that makes the family SPR. Connections between the existence of this filter and a parity interlacing property are unveiled. The degree of the solution can be a priori bounded and depends on the number of crossings of the unwrapped phases of the two extremal plants. The synthesis procedure is an adaptation of the Youla-Saito algorithm (1967)