An efficient model reduction strategy for discrete-time index-2 descriptor control systems

In this paper, we present an efficient algorithm for model reduction of discrete-time index-2 descriptor systems arising in context of linear time invariant (LTI) control and stability of descriptor systems. We propose a Smith-based iterative method for the model order reduction (MOR) strategy which consists of two stages. In the first stage, we reformulate the descriptor system into a generalized system by manipulating its system structure. Once the reformulated generalized system is obtained, it is amenable to a balanced truncation-based model order reduction strategy. The second stage of our work focuses on solving the generalized discrete-time algebraic Lyapunov equations (DALES) associated with the generalized system. Smith iterations are implemented to compute the solutions to these Lyapunov equations. Results from various numerical simulations are included to corroborate the high performance and accuracy of the proposed algorithms.