Balanced truncation for unstable infinite dimensional systems via reciprocal transformation

We discuss a model reduction for unstable infinite dimensional systems using balanced truncation of reciprocal systems. The systems considered are assumed to be exponentially stabilizable and detectable, with bounded and finite rank input and output operators. We decompose the systems into their stable and unstable parts and perform reciprocal transformation only on the stable part. Balanced truncation is carried out on the reciprocal systems. This yield is then translated using reciprocal transformation as the reduced-order model of the stable part. Finally, we added the unstable part to the reduction of the stable part as the overall reduced-order model for the systems. To verify the effectiveness of the proposed approach, numerical simulations are applied to the heat equation. The performance of the proposed reduction method is compared to the balanced truncation method.