2-D model reduction by quasi-balanced truncation and singular perturbation

This paper considers two-dimensional system model reduction using 2-D balanced truncation and singular perturbation. A new 2-D state space realization named quasi-balanced realization is proposed which is closely related to a pseudo-balanced realization and a structurally balanced realization. A unique feature of the new balanced realization is that it is numerically efficient when it exists and it reduces to the pseudo-balanced realization if the system is denominator separable. An improved frequency error bound is also derived for the pseudo-balanced (or quasi-balanced) realization model reduction for denominator separable systems. Finally, a new 2-D model reduction method together with stability analysis based on singular perturbation theory is studied