Stability and stabilisation of linear multidimensional discrete systems in the frequency domain

Abstract

This paper gives a reasonably detailed review of advances in stability and stabilisation of linear multidimensional (N-D) discrete systems in the frequency domain. The emphasis is on the recent progress, especially in the past decade. The discussion will focus on two topics: (i) stability test. Determination of whether a given N-D (N ≥ 2) system is stable; (ii) stabilisation. Parameterisation of all stabilising compensators for a stabilisable N-D system. After reviewing the progress and several state of the art methods in these two topics with illustrative examples, some related issues are also briefly mentioned at the end.

Keywords:

• multidimensional systems
• stability
• stabilisation
• parameterisation

Notes

1. Throughout this section, the term ‘N-D’ implies N ≥ 3 unless otherwise indicated.