A Unified Proof of the Characteristic Model of Linear Time-Invariant Systems

The characteristic modeling problem of linear time-invariant systems is addressed in this paper. It is proved that the characteristic model of the MIMO linear time-invariant systems can be expressed by a time varying difference equation of order 2. The modeling error of characteristic model is discussed. When there is not zero real part pole in the plants, the transient modeling error is O(h) and the steady modeling error is O. In the general cases, the transient modeling error is O(h) and the steady modeling error is O(h²). The proof indicates that the characteristic model is essentially different from the conventional reduced-order model. It compresses all the information of the system dynamics into several characteristic parameters. In the bandwidth of control system, no information is lost.