Fast identification of state-space models via exploitation of displacement structure

A novel fast algorithm for the identification of state-space models is presented. This approach exploits the displacement and low-rank plus shift structures of the matrices that arise in the identification procedure to reduce the computational cost from O(MN²+NM²+M ³) to O(MN+M²) flops, and storage from O(M²+MN+N²) to O(N+M²) bytes. Such reductions of computational burden and storage requirement may allow online identification of state-space models in many potential applications. The proposed identification technique was applied to a two-input, two-output simulated system to validate the algorithm