Qualitative stability concept from ecology and its use in the robust control of engineering systems

Abstract

This paper addresses the issues of qualitative stability, a topic of interest in the general field of life sciences (especially in ecology) and robust stability and stabilization of linear uncertain systems encountered in engineering sciences and proposes to develop a synergy between these two concepts by making qualitative (or sign) stability concept as a useful tool in the analysis and synthesis of robust engineering systems. It may be noted that there are many conceptual differences in the qualitative (sign) stability literature of ecology reviewed in this paper and the qualitative (sign) stability literature available in the engineering sciences. Thus the main emphasis of the paper is to highlight these differences and bring out usefulness of this concept from ecology to applications in engineering sciences. The paper first reviews the fundamentals related to 'qualitative (or sign) stability' of ecology including the necessary and sufficient conditions for qualitative stability. Then the problem of robust stability and stabilization of linear uncertain systems is addressed and the use and implications of these qualitative stability ideas in various engineering applications is discussed. In addition, a new, robust controller synthesis using these sign stability ideas of ecology is illustrated for the applications of satellite formation flying control and three axis satellite attitude control. It is concluded that qualitative stability concept from ecology (of life sciences) can be further exploited to solve many other interesting problems in engineering sciences.