Stabilization by Controllers Having Integer Coefficients

TL;DR

This paper proves the existence of integer-coefficient controllers for stabilizing discrete-time LTI plants, providing a constructive method to obtain such controllers and demonstrating their application in preserving system performance.

Contribution

It introduces a constructive algorithm for designing integer-coefficient stabilizing controllers and applies it to convert existing controllers without performance loss.

Findings

Existence of integer-coefficient stabilizing controllers proven.

A constructive algorithm for controller design provided.

Method preserves original system performance during conversion.

Abstract

The system property of ``having integer coefficients,'' that is, a transfer function has an integer monic polynomial as its denominator, is significant in the field of encrypted control as it is required for a dynamic controller to be realized over encrypted data. This paper shows that there always exists a controller with integer coefficients stabilizing a given discrete-time linear time-invariant plant. A constructive algorithm to obtain such a controller is provided, along with numerical examples. Furthermore, the proposed method is applied to converting a pre-designed controller to have integer coefficients, while the original performance is preserved in the sense that the transfer function of the closed-loop system remains unchanged.