Strong Kharitonov theorem for discrete systems

Necessary and sufficient conditions for the stability of discrete systems with parameters in a certain domain of the parameter space are derived. The result is the analog of Kharitonov's strong theorem. Two methods are used to arrive at this result, one by projecting the roots of the symmetric and the asymmetric part of the polynomial f(z) on the [-1, +1] line. The resulting Chebyshev and Jacobi polynomials give certain intervals on the [-1, +] line. In each interval it is necessary to check the four corner polynomials corresponding to Kharitonov's strong theorem for continuous systems. The number of intervals increases with the degree ov the polynomial. The other method is the frequency-domain method where the intervals are easily obtained through the roots of trigonometric functions. A recursion formula is derived and the number of intervals is shown to be a sum of Euler functions.