Orthonormal Representations for Output System Pairs

A new class of canonical forms is given proposed in which (A,C) is in Hessenberg observer or Schur form and output normal: I − A∗A = C∗C. Here, C is the d × n measurement matrix and A is the advance matrix. The (C,A) stack is expressed as the product of n orthogonal matrices, each of which depends on d parameters. State updates require onlyO(nd) operations and derivatives of the system with respect to the parameters are fast and convenient to compute. Restrictions are given such that these models are generically identifiable. Since the observability Grammian is the identity matrix, system identification is better conditioned than other classes of models with fast updates. AMS Classifications: 93B10, 93B11 93B30