A lower bound for H∞-optimal performance

Computing the H_∞ mixed sensitivity optimal performance has been shown to be equivalent to computing the norm of a Hankel+Toeplitz type operator (see E. Jonchkheere and M. Verma, 1986). The essential spectral radius of the operator provides a lower bound for the operator norm, and it therefore provides a lower bound for the H^∞ mixed sensitivity optimal performance. Motivated by an infinite-dimensional multi-input/multi-output (MIMO) practical control model, the authors derive an explicit formula for the essential spectra for the related Hankel+Toeplitz type operators. The formula is a generalization of that of G. Zames and S. Mitter (1988)