Sufficient Conditions for Stabilizability by Discrete-Time Controllers Possessing Monic Characteristic Polynomials With Integer Coefficients
Mohammad Saleh Tavazoei · IEEE Control Systems Letters · 2023
Considering the desirable feature of possessing an infinite lifespan for discrete-time controllers having integer monic characteristic polynomials in partially homomorphic encrypted environments, this paper deals with obtaining sufficient conditions to guarantee that stabilizability by such controllers is possible. Firstly, a linear programming based stabilizability condition is derived for the special case that the controller is described by an FIR model. Then, benefiting from the Minkowski theorem in geometric number theory, a sufficient condition for stabilizability by non-FIR controllers with integer monic characteristic polynomials is obtained.