DYNAMICAL-SYSTEMS THAT COMPUTE BALANCED REALIZATIONS AND THE SINGULAR-VALUE DECOMPOSITION

The tasks of finding balanced realizations in systems theory and the singular value decomposition (SVD) of matrix theory are accomplished by finding the limiting solutions of differential equations. Several alternative sets of equations and their convergence properties are investigated. The dynamical systems for these tasks generate flows on the space of realizations that leave the transfer functions invariant. They are termed isodynamical flows. Isodynamical flows are generalizations of isospectral flows on matrices. These flows evolve on the actual system matrices and thus remove the need for considering coordinate transformation matrices. The methods are motivated by the power of parallel processing and the ability of a differential equations approach to tackle time-varying or adaptive tasks.