On the Strictly-Positive-Realness of Schur Interval Functions

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. SPR interval functions play an important role in the stability of adaptive control systems, 2-dimensional systems, and delay differential systems, as well as in the convergence analysis of adaptive digital signal processing and identification algorithms.