FIR Stabilizability Ensures Stabilizability by Non-FIR Controllers Having Integer Monic Characteristic Polynomials

To avoid computational overflow in partially homomorphic encrypted control systems with dynamic LTI discrete-time controllers, it has been previously suggested to use controllers possessing integer characteristic polynomials. These controllers are divided into two categories: FIR controllers and non-FIR ones. In this paper, it is proved that each plant, which is stabilizable by FIR controllers, can be also stabilized by non-FIR ones having integer characteristic polynomials. Furthermore, the validity of this statement is verified by numerical examples. The theoretical achievement of this paper reveals the existence of a degree of freedom to choose between FIR controllers and non-FIR ones, when the aim of the control system designer is to use a dynamic controller with integer characteristic polynomial in partially homomorphic encrypted environments for avoiding computational overflow.