Recently, it has been observed that finite impulse response controllers are an excellent basis for encrypted control, where privacy-preserving controller evaluations via special cryptosystems are the main focus. Beneficial properties of FIR filters are also well-known from digital signal processing, which makes them preferable over infinite impulse response filters in many applications. Their appeal extends to feedback control, offering design flexibility grounded solely on output measurements. However, designing FIR controllers is challenging, which motivates this work. To address the design challenge, we initially show that FIR controller designs for linear systems can equivalently be stated as static or dynamic output feedback problems. After focusing on the existence of stabilizing FIR controllers for a given plant, we tailor two common design approaches for output feedback to the case of FIR controllers. Unfortunately, it will turn out that the FIR characteristics add further restrictions to the LMI-based approaches. Hence, we finally turn to designs building on non-convex optimization, which provide satisfactory results for a selection of benchmark systems.

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