A numerical method for computing signature symmetric balanced realizations

Computation of Signature Symmetric Balanced Realizations

A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of th...

On reciprocal systems and controllability

In this paper, we extend classical results on (i) signature symmetric realizations, and (ii) signature symmetric and passive realizations, to systems which need not be controllable. These results are motivated in part by the existence of important electrical networks, such as the famous Bott-Duffin networks, which possess signature symmetric and passive realizations that are uncontrollable. In ...

Educational Article:Gramians and Balanced Realizations and their Application in System Order Reduction

Educational Article:Gramians and Balanced Realizations and their Application in System Order Reduction

Symmetric singular linear control systems

using the group inverse, an explicit solution to a symmetric singular system is described. The general explicit solution is derived when the symmetric singular system satisfies the regularity condition. Certain special properties of these singular systems are presented. Finally, a symmetric balanced realization is obtained from an equivalent standard control system. @ 2002 Elsevier Science Ltd....