Model reduction for singular systems via covariance approximation

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