ON BALANCING AND ORDER REDUCTION OF UNSTABLE PERIODIC SYSTEMS

摘要

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.