Generalized model for linear systems reduction



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A control system, in general, could consist of hundreds of elements. Therefore considering the vastness of control systems, control engineers have to face three different problems such as: (1) the variables are too many to handle; (2) the dimension of the system is too high to comprehend; and (3) the modifications required of the goals for the design are difficult to ascertain. The normal procedure is to seek methods which reduce the order of a transfer function or decrease the dimension of a state equation. This thesis attempts to develop a new model for the reduction and approximation of high order linear systems, taking into account not only the performance of the system in the low frequency region (steady state response), but also the performance of the system in the high frequency region (transient response). A Continued Fraction Expansion which is a combination of the First and Second Cauer Forms is used for the reduction of the rational and transcendental transfer functions.