Model Reduction of Time-Varying Descriptor Systems

The book presents two important approaches for model reduction of periodic time-varying descriptor systems. The Krylov subspace based projection technique and the balancing based projection technique have been used for model reduction of time-varying descriptor systems. We proposed the recycled Krylov subspace method to approximate the appropriate subspaces for model reduction of continuous-time periodic descriptor systems. We have also shown that due to the shift-invariance property, the approximation scheme for multiple frequency points becomes much simpler and faster. A balanced truncation model reduction method is proposed for periodic discrete-time descriptor systems. We have solved the lifted Lyapunov equations for the periodic Gramians to find a reduced model of the original system. The iterative techniques, such as the Alternating Direction Implicit (ADI)method and the Smith method are also proposed for such model reduction procedure. We have shown numerical results using real data to illustrate the efficiency and accuracy of the proposed methods.