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This paper proposes a theory for designing stable interconnection of linearactive multi-port networks at the ports. Such interconnections can lead tounstable networks even if the original networks are stable with respect tobounded port excitations. Hence such a theory is necessary for realisinginterconnections of active multiport networks. Stabilization theory of linearfeedback systems using stable coprime factorizations of transfer functions hasbeen well known. This theory witnessed glorious developments in recent pastculminating into the $H_{\infty}$ approach to design of feedback systems.However these important developments have seldom been utilized for networkinterconnections due to the difficulty of realizing feedback signal flow graphfor multi-port networks with inputs and outputs as port sources and responses.This paper resolves this problem by developing the stabilization theorydirectly in terms of port connection description without formulation in termsof signal flow graph of the implicit feedback connection. The stable portinterconnection results into an affine parametrized network function in whichthe free parameter is itself a stable network function and describes allstabilizing port compensations of a given network.

Stabilization Theory for Active Multi Port Networks