Robust stabilization of `diamond´ plants

For continuous-time systems the robust stability problem according to which coefficients of a characteristic polynomial vary in a diamond can be considered as a dual problem to Kharitonov´s (1978, 1979) theorem on interval polynomials. The authors study the problem of the robust-stabilization of such a family of diamond polynomials. It is shown that to stabilize a family of polynomials whose coefficients of numerator and denominator lie in two diamonds is equivalent to stabilizing simultaneously sixty-four one-dimensional edges of the diamond polynomials. The result obtained is sufficient and necessary. When the variation of the coefficients is limited to denominator (or numerator) the number of edges to be checked will reduce to eight