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I am designing a controller for a system using several methods, one of which is a discrete method. In the continuous time I am looking at a logarithmically spaced frequency grid in the range $$\omega \in [0.1,1]$$Now I want to design a controller in the discrete time, but I want to evaluate the h-infinity norm (which I am minimizing) over the same frequency grid as in the continuous time.

How can I minimize the norm over the same frequency grid in discrete time?

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If I understood that right, you are trying to minimize the infinity norm over a discrete set of points. If that is the case you set over which you are trying to minimize is not convex and this is very much a NP hard problem, unless the set is very small, so that we can rigorously loop over it. Those are my thoughts on this.

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