Algorithms for model order reduction of structured periodic control system and simulations of results

This paper is concerned with the structurepreserving iterative approach to reduction index-2 periodic models descriptor systems with the aid of generalized inverses of periodic matrix pairs. At the beginning of our work, we modify the system structure in order to reformulate a discretetime descriptor system into a discrete-time generalized system. The system is then represented by a cyclic lifted structure, with the generalized inverses of the periodic matrix pairs computed. Smith’s method is exploited to find the iterative solutions of the associated Lyapunov equations of the cyclic lifted system. Solutions of these Lyapunov equations consist of the solutions of the periodic Lyapunov equations of the original periodic system. The periodic system is then reduced by using projectors computed from those periodic solutions. The above procedures are applied to reduce the artificial problem of an index-2 periodic structure. To verify the performance and accuracy of the algorithm we included the results from numerical simulations.