Computational aspects of gain-frequency response for sampled-data systems

This paper addresses the computational aspects of the frequency response for sampled-data systems. We first give two types of lower bound formulas. The first is derived via fast sampling of the input functions and the second is derived via the dual system. It is shown that as the fast sampling period approaches zero, these lower bounds converge to the gain. Two different formulas for upper bounds are also obtained. One is based on the information about the closed-loop poles, and another relates the gains of the ℋ₂ norm equivalent discrete-time system. We then discuss the bisection search. It is seen that where certain non-degeneracy condition holds, bisection search is possible, some comparisons are made with numerical examples