On the identification of linear time-invariant systems

A new canonical form of state variable equations (for a linear time-invariant system) is developed. This canonical form has the specialty that the state variables can easily be generated using the integrals of the input and the observable ouput. This special property can be exploited to identify the parameters of the unknown system. If the system whose parameters are to be determined, is found to be stable, identification of the parameters is shown to be very simple. Non-zero initial conditions are handled very easily by a proper choice of the input (excitation) function. The calculation of the unknown parameters involves the determination of integrals (with the consequent suppression of any effect of measurement noise) and solution of a linear system of algebraic equations. It is not necessary, theoretically at least, to assume the order of the unknown system to be identified. The proposed method of identification, it is believed, adapts itself in the development of a lower order approximate model for the unknown system.