Model-order reduction for differential-algebraic equation systems with higher index

Optimal Hankel norm model reduction for discrete-time descriptor systems

“…Other types of the balanced truncation method such as positive real and bounded real balancing, stochastic balancing and LQG balancing are proposed in [9,12,13] , respectively. From the viewpoint of interpolating the transfer function, Krylov subspace methods are extended to descriptor systems in [14,15] . One problem of the interpolation-based methods is the selection of the interpolation points and the interpolation directions for multi-input multi-output (MIMO) systems in the tangential interpolation scheme [16] .…”

“…. M 1 M 0 with M i given by (15) and The state-space representation (25) is in a controllable canonical-type form. It can be easily checked that the impulse response is preserved by such a realization.…”