On the Stability of Linear Dynamic Controllers With Integer Coefficients
Nils Schlüter, Moritz Schulze Darup
Abstract
In this article, we show that linear dynamic controllers with integer coefficients are usually unstable. In fact, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero. Moreover, for a fixed controller order, there exist only finitely many characteristic polynomials with integer coefficients that lead to marginally stable eigenvalues on the unit circle and we characterize these setups. The obtained results are, in particular, relevant to encrypted control, where (nontrivial) stable controllers with integer coefficients were on the “wish list.”
Topics & Concepts
Integer (computer science)Eigenvalues and eigenvectorsMathematicsControl theory (sociology)Controller (irrigation)Stability (learning theory)Unit circleExponential stabilityLinear systemApplied mathematicsCombinatoricsMathematical analysisControl (management)Nonlinear systemComputer sciencePhysicsProgramming languageAgronomyMachine learningBiologyArtificial intelligenceQuantum mechanicsSecurity in Wireless Sensor NetworksQuantum chaos and dynamical systemsCryptography and Data Security