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Abstract
In this paper we derive a differential-difference equation for a circuit involving a lossless transmission line and we give conditions for global asymptotic stability of an equilibrium point, existence and stability of forced oscillations. Some of such problems have been investigated for an equation obtained by R. K. Brayton [ Quart. J. Appl. Math. 24 (1967) , 289–301; O. Lopes, SIAM J. Appl. Math., to appear; M. Slemrod, J. Math. Anal. Appl. 36 (1971) , 22–40] but, for ours (which governs the same physical problem), better results can be proved. By using suitable Liapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality.
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