Enhancing Strict Positive Realness Condition on Families of Polynomials by Filter Design

In this paper some results on strict positive realness of families of polynomials are given. The main motivation for these results is the need, for design criteria of filters ensuring convergence of algorithms in the presence of uncertainty in the plant model in the area of identification and adaptive control. Two main results are given in the paper. The first result provides analytical conditions under which a family of polynomials with zeros in a prescribed region of the complex plane is strict positive real or can be made strict positive real over an assigned region of the complex plane through the use of a suitable filter. The second contribution is a design result providing a parameterization of a family of filters maximizing the region of the complex plane on which strict positive realness is achievable.