Balanced Reduction for a Class of Time Delay Systems

Abstract

A calculation method of Hankel singular values is discussed for input and unilateral time delay systems. For input time delay systems, whose channels involve different value of time delays independently, the Hankel singular values are obtained based on a matrix Lyapunov equation. By introducing auxiliary systems for the unilateral time delay system, it is shown that the singular values are characterized based on the preliminary results for input time delay systems. When Hankel singular values and vectors are derived for input and unilateral time delay systems, the calculation method of balanced reduction is constructed. We investigate balanced reduction with numerical examples.