| The allowable parameter variations for a linear system are analysed from the parameter space approach. By using the method of frequency scaling, the largest hyperspheres in the coefficient space for a family of stable continuous polynomials are extended to hyperellipsoids. In another approach, the largest hyperrectangle with given shape in the coefficient space for a family of stable continuous polynomials is found. This approach is then extended to a set of discrete polynomials with varying "lower-half" coefficients. For a set of discrete polynomials in which all coefficients can vary, a family of largest rectangles are determined in a set of specified coefficient planes. Finally, a quantitative measure of allowable perturbations to a system matrix is obtained by finding the largest hypersphere centered at the nominal system matrix in the parameter space. |
