A new approach to the robust stability analysis and to the robust controller design is proposed via reflection coefficients of characteristic polynomials of discrete-time systems. The reason of using reflection coefficients instead of roots of the characteristic polynomial is that the mapping between reflection coefficients and polynomial coefficients is multilinear. So we can easily find some Schur stable line segments in the polynomial coefficient domain by varying a single reflection coefficient. The more serious task is: how to find a convex subset of the stability region in system parameters domain.

Two problems are considered: first, a stable polytope building around a given stable point and, second, a robust controller design via stable convex sets. The first problem is solved starting from so-called reflection vectors of a special family of Schur stable polynomials. Roots placement of reflection vectors is studied and the volume of stable reflection vector polytopes is calculated.

The robust controller design problem is formulated as a stability margin maximization task over the convex approximation of the stability region. If this convex approximation is given as a stable polytope then the problem of robust output controller design is solved by a quadratic programming approach.

Future research will focus on the robust state feedback controller design.

We have international cooperation and joint publications with prof. R. Luus (Univ. of Toronto).