
Accession Number : AD0634272
Title : ALGEBRAIC GENERATION AND ACTIVE NETWORK REALIZATION OF STATE EQUATIONS,
Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB
Personal Author(s) : MARTENS, G. O.
Report Date : MAY 1966
Pagination or Media Count : 63
Abstract : A characterization is given for the state equations of an RLC network with sources. It is shown that the coefficient matrix of the state equations must be representable as a product of two factors satisfying necessary symmetry conditions. Each factor must be realizable as the inputoutput matrix of a resistive network. It is also shown that, except for degenerate cases, an inputoutput matrix singular as well as nonsingular must satisfy a divisibility property. The divisibility property is then utilized to insert variables to generate a nearprimitive hybrid matrix from an inputoutput matrix. This process is algebraic and does not require the factoring of polynomials. The nearprimitive hybrid matrix determines a positive definite diagonal matrix and a hybrid matrix which, after the permutation of submatrices, yield the required product representation for the coefficient matrix of the state equations. The characteristic polynomial of the A matrix is identical with the minimal polynomial of A and the monic common denominator of the inputoutput matrix. Active RC and active RLC network realizations for timevarying as well as timeinvariant linear state equations are obtained. Thus it is shown that any linear system, timevarying or timeinvariant, can be simulated by an active network. (Author)
Descriptors : (*ELECTRICAL NETWORKS, *MATRICES(MATHEMATICS)), INPUT OUTPUT DEVICES, EQUATIONS OF STATE, SYNTHESIS, DYNAMICS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE