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Linear systems with irrational transfer functions are difficult to simulate in the time domain. We consider causal systems which can be represented with poles and cuts in some left half-plane of the Laplace domain. Whereas standard interpolation methods yield convergent but high-dimensional approximations, it is possible to derive efficient low-cost approximations thanks to optimization procedures. Defining the criterion (choice of weightening measure, regularization and contraints) is however of utmost importance: this must be carefully designed and driven by each application. Two examples will illustrate the methodology, and a third one will present an extension to a compound system with delays.