Robustness analysis via Tchebyshev representations

We develop some new techniques for the computation of stability margins under parameter variations for discrete time systems. This is based on representing the unit circle image of a real polynomial in terms of Tchebyshev polynomials. The Tchebyshev representation leads to simple formulas for stability margin computation. We specifically develop a method of verifying the Schur stability of a line segment and also compute the parametric stability margin of a parameter vector, centered around a nominal value. Potential applications of the Tchebyshev representation are discussed