Abstract
We consider the numerically reliable computation of reachability and observability Kalman decompositions of a periodic system with time-varying dimensions. These decompositions generalize the controllability/observability Kalman decompositions for standard state space systems and have immediate applications in the structural analysis of periodic systems. We propose a structure exploiting numerical algorithm to compute the periodic controllability form by employing exclusively orthogonal state-space similarity transformations. The new algorithm is computationally efficient and backward stable, thus fulfils all requirements for a satisfactory algorithm for periodic systems.
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