STATE-SPACE MODEL IDENTIFICATION OF UNSTABLE LINEAR-SYSTEMS

A new state space model identification algorithm for unstable linear systems is proposed in this paper. By using a linear transformation and a possibly unbounded input sequence, the numerical difficulty which persists in the parameter estimation of unstable systems can be alleviated. It is shown that under such a transformation, the equivalent input sequence will still be persistently exciting under a rather mild condition. Therefore, the identification of all unstable modes is guaranteed after the transformation. The use of numerically stable singular value decomposition and the possibility of using long data records to reduce the identification bias ensued by noise are other features of the algorithm.