ABSTRACT

This chapter addresses classical identification theory, and in particular its connections to Hankel forms and the Beurling-Lax theorem. It reviews classical identification theory. Virtually all known methods in identification theory can be reduced to a common strategy: adjust the parameters of a vector until it lies in the null space of a Hankel form built from the system to identify. The chapter identifies the system. This interpretation is compatible with the Ho-Kalman formulation, but has gone virtually unnoticed in classical identification theory. The chapter considers only three approaches: Pade approximants, equation-error approximants, and L2 output-error approximants. It suggests that other methods of adaptive infinite impulse response (IIR) filtering also fit into this context, notably the Steiglitz-McBride method and hyperstability approaches. The chapter illustrates the word "approximate" here that has a direct connection with the approximation criterion used. It examines some classical methods for identification of a linear system, and reconciles such approaches with Kronecker's theorem and the Beurling-Lax results.