Computation of the frequency response gains and H ∞ -norm of a sampled-data system

Abstract This paper presents a method for computing the frequency response gains and H ∞ -norm ( L 2 -induced norm) of a sampled-data system composed of continuous-time and discrete-time systems together with a sampler and a hold. The method is based on the notion of FR-operator, and uses only such elementary frequency-domain notions as (conventional) z -transformation, pulse transfer function and impulse modulation formula, while the numerical computations can be carried out using state-space equations. This method turns out to have a natural parallelism to the usual methods for continuous-time and pure discrete-time systems, and the frequency response gain at each frequency can be computed to any degree of accuracy in a numerically reliable fashion.

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