Orthogonal functional approximations to linear dynamical systems

A method is described for the synthesis of a dynamical model of a linear system, based on the use of orthogonal and, in particular, orthonormal functions. It is shown that, if the nominal values of all poles of a system are known, and only one pole changes from its nominal value, this change may be detected. It is also demonstrated that the numerator terms of the transmission transfer function of the system may be found, provided that the denominator is known. Active networks are described for the simulation of the relevant orthonormal functions. The results of some experimental investigations are discussed, and it is demonstrated that an approximate model may be synthetised of a linear system, in which three poles change simultaneously from their nominal values, but in a time which is long compared with that of the measurements involved in detecting these changes.