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, +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 of 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