An efficient algorithm for reduce order modeling of discrete-time index-2 descriptor control systems

Abstract

We have presented an efficient approach for reduce order modeling of discrete-time linear time-invariant (DT-LTI) index-2 descriptor systems which arise in the study of control system. This paper is a follow up and advancement of our previous work [1]. The contribution of this paper lies in finding the projection free model order reduction (MOR) strategy for the index-2 linear descriptor systems. Instead of reformulating the descriptor system into a generalized system as of [1], we propose a simpler and more efficient MOR strategy where balanced truncation can be applied only in the finite parts of the matrices. We derive an unique method analogous to the Smith iteration method in order to solve the generalized discrete-time algebraic Lyapunov equations (DALEs) without explicitly computing the projection matrices. Finally, we confirm the accuracy and better efficiency of our proposed algorithm with the help of results acquired from numerical simulations.