Development of model reduction technique for weighted and limited-intervals gramians for discrete-time systems via balanced structure with error bound

Enns’s weighted and Gawronski and Juang’s limited-interval scheme produce unstable reduced-order models for original stable discrete-time systems. To the best of the author’s knowledge, there is no literature available to overcome these main drawbacks in time-weighted and limited-time intervals. In this article, the time-weighted and limited Gramians intervals-based model order reduction framework is proposed for the stable discrete-time system. The proposed framework guarantees the stability of the reduced-order model. It also ensures that a low approximation error is achieved in the desired weights and limited-time intervals and an easily calculable a priori error-bound expression. Simulation outcomes show that the proposed framework provides satisfactory and accurate performance, indicating its usefulness.