Analysis and filter design for strict positive realness of families of polynomials

Some results on strict positive realness of families of discrete polynomials are given. The main motivation is the need in the area of identification and adaptive control for design criteria of filters ensuring convergence of algorithms in the presence of uncertainty in the plant model. Two main results are given. 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 and enjoying other optimality properties, such as order minimality.<>