Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems
Provides theoretical guarantees and computational strategies for model order reduction in finite time intervals, benefiting control and signal processing applications.
This paper develops error bounds for time-limited balanced truncation of discrete-time systems and proposes efficient numerical methods for large-scale implementation.
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the approximated output vector within the time limits. The influence of different components in the established bounds will be highlighted. After that, the second part of the article proposes strategies that enable an efficient numerical execution of time-limited balanced truncation for large-scale systems. Numerical experiments illustrate the performance of the proposed techniques.