Synthesis of Impulse Response Matrices by Internally Stable and Passive Realizations

A class of realizations (termed uniform realizations) for time-variable impulse response matrices is defined which plays a role similar to that of minimal (completely controllable and observable) realizations for time-invariant systems; members of the class have bounded coefficients and are uniformly asymptotically stable if the impulse response matrix represents a bounded-input boundedoutput (BIBO) stable system. The necessary and sufficient conditions for an impulse response matrix to be uniformly realizable are derived together with an explicit realization procedure. Sufficient conditions for a system to be realizable as a passive network are also obtained, and it is shown that any BIBO-stable uniformly realizable impulse response matrix may be synthesized as the transfer response of a passive network composed of constant positive inductors and resistors and bounded time-variable gyrators.