On Balancing and Order Reduction of Unstable Periodic Systems

Abstract: We consider the direct application of balancing techniques to unstable periodic systems by extending the balancing concepts to arbitrary periodic systems. We extend first the balancing concepts to unstable discrete-time systems by defining the reachability and observability grammians from appropriate right and left coprime factorizations with inner denominators. Further, we extend this new balancing method to unstable linear time-varying discrete-time systems with periodically varying coefficient matrices. The new balancing approach serves as basis to develop balancing related order reduction methods for unstable periodic systems using accuracy enhancing square-root and balancing-free algorithms