Time-Varying Networks, I

This paper presents an analysis of some of the significant developments in time-varying network theory which have taken place during the past decade, with the emphasis placed on three topics: 1) characterization of time-varying networks, and in particular, transition from the impulsive response to the differential equation; 2) the problem of factorization, with emphasis on the contributions of Darlington, Batkov and Paul Levy; and 3) randomly-varying systems and, in particular, the question of stability of discrete-time systems of this type. The identification problem, the analysis of periodically-varying systems, the synthesis problem, and the filtering and prediction of nonstationary processes will be treated in Part II, to be published later.