On generating random systems: a gramian approach

A new procedure for computer generation of random stable, linear, time invariant systems in state space form is described. Controllability and observability gramians are randomly generated according to a desired distribution. Then, a system which has the generated gramians is found. This new random system generation method is compared to several other methods using empirically observed distributions on Hankel singular values, eigenvalue magnitudes, and controllability/observability gramian condition numbers.