Model reduction of singular systems via covariance approximation

Model reduction problem was investigated for singular systems. To solve the problem, the covariance for singular systems was defined. Then, a model reduction method based on covariance approximation was presented for obtaining stable and impulse controllable models for singular systems. Thirdly, the error criterion was explicitly derived via a free parameter and the optimization procedure was presented in terms of gradient flow. Finally, illustrative examples were given to show the effectiveness of the proposed approach.