K-cyclic Smith iterative method for model reduction of index-2 periodic control systems

In this paper, we present a structure preserving Smith based iterative method for the model order reduction of index-2 periodic descriptor systems. The work of this paper is twofold. The first half of our work focuses on reformulating a discrete-time descriptor system into a discrete-time generalized system by manipulating the system structure. Once the transformed generalized system is obtained, it is expressed in a cyclic lifted representation to make it into the framework for balanced truncation-based model order reduction. The latter half of our work is dedicated to the application of our proposed Smith based algorithm to estimate the solutions of the lifted discrete-time algebraic Lyapunov equations (LDALEs) associated with the system. Cyclic permutation strategies are employed in our proposed algorithm which allows us to hold onto the original block diagonal structure of the solution in the iterative computations. The efficiency and accuracy of our proposed algorithm is verified using results obtained from numerical simulations.