H-infinity Balanced Truncation Method for Model Reduction of Differential-Algebraic Systems

In this paper, by two H∞ generalized algebraic Riccati equations ,we generalize the method of H∞ balanced truncation to the problem of model reduction of linear time-invariant continuous-time differential-algebraic equations (descriptor systems) and we also derive the error of between the reduced system and the original system by using the so-called gap metric. On the other hand, we give and prove a new theorem, Zero-D theorem. According to this theorem, for any given linear time-invariant continuous-time descriptor system with D ≠ 0, it can be equivalent to another linear time-invariant continuous-time descriptor system with D = 0.