On lower bound for anisotropic norm of linear stochastic stationary system

The anisotropic norm of a linear discrete time invariant system is a measure of system output sensitivity to stationary Gaussian input disturbances with mean anisotropy bounded by some nonnegative parameter. The mean anisotropy characterizes the predictability degree of stochastic signal. The anisotropic norm of a system is an induced norm, limiting cases of which are $\mathcal H_2$- and $\mathcal H_\infty$-norms as $a\to0$ and $a\to\infty$, respectively. This paper develops a new method for getting the lower bound for anisotropic norm by linear algebra standard methods.