A dual reduction strategy for reduce-order modeling of periodic control system

Abstract

Model order reduction (MOR) of periodic systems using the Krylov subspace methods received lots of interest in last few decades. In this paper, a structured Krylov subspace based model reduction for linear discrete-time periodic (LDTP) control system has been proposed using the corresponding lifted form. The proposed model reduction strategy first finds a reduced order Lyapunov equation via a projection where the projection subspace is computed by using the periodic Arnoldi method. Then, by applying the balanced truncation model reduction approach, it forms a reduced order model of the original system. In both cases, the periodic structure is ensured in the solutions and systems’ dynamics. This paper also presents numerical results to confirm the efficiency and accuracy of the proposed algorithm.

Keywords

• Linear discrete-time periodic systems
• Lifted state space representation
• Periodic Lyapunov equations
• Structured Krylov subspace
• Model order reduction