On the Identification of Linear Time-Invariant Systems from Input-Output Data

DEVOTED T O T H E S C I E N T I F I C AND E N G I N E E R I N G ASPECTS O F ELECTRICAL C O M M U N I C A T I O N May-June 1969 American Telephone and On the Identification of Linear Time-Invariant Systems from Input-Output Data By B. GOPINATH (Manuscript received December 17, 1968) This payer presents a new method for computing the parameters which determine the differential equations governing a linear time-invariant system with multiple inputs and outputs. Unlike earlier approaches the method presented does not involve computation of the impulse response. One of the main advantages of this method is its easy generalization to the case when the given data is contaminated with noise. The identification of multiple input-output linear systems has been a problem of considerable interest because of its importance in circuit and control system theory. In circuit theory the problem is that of synthesizing a linear time invariant circuit to exhibit a prescribed input-output behavior. In control theory, however, the problem arises out of a need to model a given linear system with a suitable set of differential equations, given its input-output behavior. References 1, 2, and 3 deal with the problem of determining the parameters of the differential equation model from the impulse response. To the best of the author's knowledge, there is no published method which determines the impulse response from a finite segment of input-output data in the case of systems with more than one input and output.