Singular Perturbation Approximation of Balanced Infinite-Dimensional Systems

This paper concerned with a model reduction of infinite dimensional systems by using the singular perturbation approximation. The system considered is that of the exponentially stable linear system with bounded and finite-rank input and output operators such that the balanced realization can be performed on the system. Furthermore, the singular perturbation method is applied to reduce the order of the balanced infinite dimensional systems. A reduced-order model can be obtained by setting to zero of derivative all states corresponding to smaller Hankel singular values. To show the effectiveness of the proposed method, numerical simulations are applied to the heat conduction.