Stability analysis of a transmission line with variable parameters

In this paper, we have presented very simple verifiable criteria for stability of a transmission line with variable (both in time and space) parameters. The system is described by a pair of hyperbolic partial differential equations with nonhomogeneous boundary conditions representing the inputs to the system and free terms representing load on the line. We have presented Lyapunov-type stability criteria indicating the conditions under which a transmission line struck by lightning or other switching surges will return to the original state or attain a new state. We have also presented two types of stability in the bounded-input bounded-output sense, one giving
L_{\infty}
. stability and the other giving
L_{2}
stability. Comments as regards implication of these results are placed in the text immediately after each result.