Overview of the recent research progress for stability and control on random nonlinear systems

Abstract

Compared with the fruitful research outcomes of stochastic nonlinear systems (SNSs) which are greatly popularised in recent decades, the research on stability analysis and control design for random nonlinear systems (RNSs) is just unfolding, which holds broader practical significance. This paper tries to provide the researchers who are interested in this realm with an overview as comprehensive as possible. In this paper, the fundamental and general framework of stability analysis for RNSs developed in (Wu, Apr., 2015) is revisited first. Then, the existing results on this subject are addressed from the perspectives of stability analysis and control design as detailed as possible based on the framework mentioned above. Next, the existing results are classified and reviewed from some specific topics and viewpoints, mainly from the class of controlled systems and the applied control schemes. Finally, the applications of the theory of RNSs are concluded briefly and a comprehensive discussion on some open problems which need future attention is presented. Nevertheless, the research outcomes on stability analysis and control design for RNSs are far from saying fruitful and systematic.