Robust performance evaluation for interval systems based on characteristic roots area

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The physical parameters of controlled systems 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. This 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's theorem (division algorithm) to the four corners of a segment polynomial. The result that is obtained by finite calculations with regard to the coefficients of the segment polynomial, can be extended to general interval polynomials with multiple uncertain parameters.

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