Singular perturbation approximation of semistable linear systems

This paper proposes a singular perturbation approximation for semistable linear systems. In particular, we derive a novel expression of error systems in the Laplace domain. As a result, we obtain an ℋ₂-error bound in terms of the sum of eigenvalues of an index matrix, which coincides with a controllability gramian of the state-derivative. Furthermore, we show that the singular perturbation model appropriately preserves the semistability of the original system and also guarantees the stability of the error system. The efficiency of the proposed method is shown through a numerical example of a Markov chain model approximation.