Nyquist, Bode, and Nichols Plots of Uncertain Systems

This paper investigates the frequency response of an uncertain system whose set of possible transfer functions is represented by a polytope of numerator-denominator polynomial pairs. It will be shown that the frequency response of the edge transfer functions provides most of the information required to determine all possible frequency responses of the system Once the edge response is computed, a simple procedure can be used to obtain the complete response. These results can be used to compute the frequency response at any point in the complex plane, so they are applicable to continuous-time and discrete-time systems. For an interval family of tansfer functions, the edge result in this paper can be combined with known properties of interval polynomials to give an even simpler method of computing the frequency response. This simplification is only valid for frequencies on the jw-axis, so its application is limited to continuous-time systems.