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Department of Mechanical Engineering
IEEE Transactions on Automatic Control, October 2022 Issue

Paper in IEEE TAC

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Illustration of eligible roots of unity © RCS ​/​ NSC

Nils Schlüter and Moritz Schulze Darup published a paper on the stability of linear dynamic controllers with integer coefficients. In particular, possible eigenvalue configurations of these special controller types, relevant for encrypted control, are investigated.

Encrypted implementations of linear dynamic controllers such as PID or observer based state feedback (for example LQG) controllers are highly relevant for practice. Unfortunately, an encrypted implementation of these controllers is not straightforward despite their simple structure. A possible solution requires the direct design of a dynamic controller with integer coefficients.

In the paper, we analyze the system theoretic properties of such dynamic integer controllers in terms of their eigenvalue configurations, which correspond to the design choices of a control engineer. Remarkably, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero and there exist only finitely many marginally stable eigenvalues. Contact Nils for further details or have a look at the paper:

N. Schlü­ter and M. Schulze Darup, On the stability of linear dynamic controllers with integer coefficients, IEEE Transactions on Automatic Control, 2021. DOI: 10.1109/TAC.2021.3131126