On the strictly positive realness of Schur interval functions

Necessary and sufficient conditions for strictly positive realness of discrete-time interval functions, which may be associated in parameter space by a multidimensional boxed domain, are provided. Positive realness of interval functions are studied, and both necessary and sufficient conditions are provided for such functions to be strictly positive real (SPR) in the presence of interval variations of the function´s parameters corresponding to a Kharitonov-type box domain. The number of checking functions that have to be tested for SPR property in order to establish the interval SPR property grows with the order of the interval function. These tests give both necessary and sufficient conditions for SPR. The approach presented for interval functions does not require the checking of all the vertices for unit circle positive realness