REPRESENTATIONS FOR CLASS K FUNCTIONS

The class k functions represent a generalization of the concept of the positive-real function. This generalization is useful for the purposes of analysis since many properties of networks, whose transfer functions are class k functions, are known. That is, if the transfer function of a network happens to be a class k function, then this transfer function and its corresponding transient responses such as the unit impulse response and unit step response will satisfy a number of restrictions. One objective of this investigation has been to construct a definition for the class k functions only in terms of the behavior of these functions in the open righthalf s-plane, as is done for positive-real functions. This will then allow such functions to have certain types of singularities on the sjw axis. It is on the basis of this more general definition of class k functions that a successful attack is made on the second and principal objective to develop a representation for class k functions, which is analogous to Cauers representation for positive-real functions. Author