Balanced Truncation Model Reduction of Nonstationary Systems Interconnected over Arbitrary Graphs

TL;DR

This paper introduces a balanced truncation method for reducing the complexity of nonstationary interconnected systems, preserving structure and providing error bounds, applicable to systems with communication delays.

Contribution

It presents a novel balanced truncation approach for discrete-time linear time-varying interconnected systems that maintains interconnection structure and reduces both temporal and spatial states.

Findings

The method guarantees interconnection structure preservation.

Upper bounds on the l2-induced norm of the error are derived.

The approach is validated through a practical example.

Abstract

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject to a communication latency of one time-step. The presented method guarantees the preservation of the interconnection structure and further allows for its simplification. In addition to truncating temporal states associated with the subsystems, the method allows for the order reduction of spatial states associated with the interconnections between the subsystems and even the removal of whole interconnections. Upper bounds on the l2-induced norm of the resulting error system are derived. The proposed method is illustrated through an example.