Abstract
For systems with uncertain parameters, stability robustness is often defined as the minimum of destabilizing parameter perturbation vectors, in the sense of a predescribed norm. The stability robustness thus defined can be visualized as the radius of the largest stability hypersphere in parameter space.
The present paper considers the stability robustness, assuming a characteristic polynomial whose coefficients are an affine function of real plant parameters. Explicit formulas are established for discretetime systems. They use two polynomials in the form of weighted sum of Chebyshev polynomials, determined from the coefficient data of the affine functions. Every hyperplane which consists of the boundary of stability region in the parameter space is found from the polynomials. Furthermore the explicit formulas would provide useful means to analyse continuity and discontinuity of the stability robustness with respect to the coefficient data.
