Abstract: | We study the spectral properties of a ‘Toeplitz+ Hankel’ operator which arises in the context of the mixed-sensitivity H∞-optimization problem and whose largest eigenvalue characterizes the optimal achievable performance ε0. The existence of such an operator was first shown by Verma and Jonckheere 26], who also'noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the ε-iteration. Here, we investigate this operator in detail, with the objective of efficiency computing its spectrum. We define an ‘adjoint’ linear-quadratic problem that involves the same ‘Toeplitz+ Hankel’ operator, as shown by Jonckheere and Silverman 13–16]. Consequently, a finite polynomial algorithm allows ε0 to be characterized as simply as the largest root of a polynomial. Finally, a computationally more attractive state space algorithm emerges from the Ht8/LQ relationship. This algorithm yields a very good accuracy evaluation of the performance ε0 by solving just one algebraic Riccati equation. Thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e-iteration. |