Absolute k-stability of linear distributed n-ports

This paper considers exclusively linear time-invariant distributedn-ports specified by a convolution operator:\breve{b} = \breve{S} \ast \breve{a}. It definesI/0stability in the time-domain and characterizes it for a broad class of suchn-ports. It characterizes absolutely stablen-ports. Finally, it defines absolutek-stability--i.e., stability of givenn-port under any loading by passivek_{1}-ports,k_{2}-ports,\cdots , k_{r},-ports, wherek_{1} + k_{2} + \cdots + k_{r} = n. The necessary and sufficient conditions for absolutek-stability are obtained using Doyle's\mufunctional. The paper is self-contained.