This paper addresses the inverse problem of anisotropy-based performance analysis of linear discrete time-invariant system. The inverse problem consists in finding the maximum level of mean anisotropy of random input sequence corresponding to some given value of anisotropic norm of system. A unique solution is determined by solving a system of four cross-coupled nonlinear algebraic equations including Riccati, Lyapunov, and two scalar equations with respect to traces of symmetric matrices