Stabilisation of discrete-time systems via Schur stability region

Abstract

In this paper, we consider the stabilisation problem of discrete-time systems by affine compensator. Using the known properties of the Schur stability region of monic polynomials, we give conditions under which stabilising controllers exist. A necessary and sufficient condition is obtained when the difference of the order of the system and the number of stabilising parameters is one. In the general case, two solution algorithms: division-elimination and least-square minimisation algorithms are suggested.