Circuits, k-ports, hidden modes, and stability of interconnected k-ports

This paper exclusively considers lumpedk-ports and circuits which contain linear time-invariant elements, independent sources, and controlled sources. Thek-ports are represented by their hybrid matrices. Tableau equations of circuits are used as a special case of polynomial matrix description. The hidden modes of a circuit are determined by inspection from its tableau equations in the Hermite row form. The same form is used also to determine the exponential stability of the circuit and that of thek-port. Finally, necessary and sufficient conditions for exponential stability of interconnectedk-ports are given; the hidden modes of the interconnection are studied. The paper is self-contained.