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

The tasks of finding balanced realizations in systems theory and the s ingular value decomposition (SVD) of matrix theory are accomplished by finding the limiting solutions of differential equations. Several alt ernative sets of equations and their convergence properties are invest igated. The dynamical systems for these tasks generate flows on the sp ace 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 sys tem matrices and thus remove the need for considering coordinate trans formation matrices. The methods are motivated by the power of parallel processing and the ability of a differential equations approach to ta ckle time-varying or adaptive tasks.