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 input-output matrix of a resistive network. It is also shown that, except for degenerate cases, an input-output matrix singular as well as non-singular must satisfy a divisibility property. The divisibility property is then utilized to insert variables to generate a near-primitive hybrid matrix from an input-output matrix. This process is algebraic and does not require the factoring of polynomials. The near-primitive 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 input-output matrix. Active RC and active RLC network realizations for time-varying as well as time-invariant linear state equations are obtained. Thus it is shown that any linear system, time-varying or time-invariant, 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