Robust strict positive realness: new results for interval plant-controller families

A frequency domain approach is used to derive several robust strict positive realness results for interval plants and interval plant plus controller families of transfer functions. Based on simple frequency domain properties of transfer functions, the approach provides a framework for obtaining new results and constructing easy proofs of several important existing results on robust strict positive realness. The main new result states that the minimum of the real part of the transfer functions belonging to an interval plant controller family is achieved on one of the 32 Kharitonov segments of the interval plant. The argument used in the proof is of wider interest and suggests easy ways of proving that robustness of other different frequency properties of interval plant plus controller families of transfer functions, such as robust stability of H_∞-norm computation, can be deduced from a fixed number of segments of transfer functions of the family