This paper considers a stable linear discrete time-invariant system with linear-fractional norm-bounded uncertainty. An estimate of the anisotropic norm of this system is derived. It is shown that the anisotropic norm is bounded above if a system of inequalities of certain kind is solvable. This system consists of two linear matrix inequalities and inequality with respect to the determinant of a positive definite matrix. By minimising the squared threshold value under constraints in form of the system of matrix inequalities one can obtain the upper estimate of the anisotropic norm of the considered system. The introduced analysis result is directly applied to solve the problem of synthesis of state-feedback robust anisotropic controller.