Some analysis tools for the design of robust strict positive real systems

This paper deals with the robust (shifted) strict positive real problem of some classes of uncertain discrete-time systems. These classes are described by rational transfer functions where the denominator (or numerator) is a fixed Schur polynomial while the numerator (or denominator) is any Schur polynomial with the roots inside a given region of the complex plane. The main result of the paper is the determination of regions of pole/zero location such that the robust strict positive real problem simply reduces to checking strict positive realness of a unique transfer function of the family. This result can be useful for the design of filters ensuring convergence of several recursive algorithms in identification and adaptive control.