A sufficient condition for characteristic roots area of interval systems

In actual systems, the physical parameters of plants are uncertain and are accompanied by nonlinearity. The transfer function and the characteristic polynomial should, therefore, be expressed by interval polynomials whether the input-output signals are continuous or discrete time. The paper examines the robust performance of that type of control system, based on the existing area of characteristic roots. In particular, a sufficient condition for the roots area which is enclosed by a specified circle on an s-plane is given by applying the classic Sturm theorem (division algorithm) to the four corners of a segment polynomial. The result that is obtained by finite calculations in regard to the coefficients of the segment polynomial, can be extended to general interval polynomials with multiple uncertain parameters.