网络稳定性与控制的小增益原理:回顾与近期进展

The small-gain theorem is one of the fundamentally important and systematic tools in modern control theory. Its power in testing robustness of stability and designing robust controllers for interconnected and uncertain systems has clearly been demonstrated in the work of many others. Taking explicit advantage of input-to-state stability(ISS), the first generalized nonlinear ISS small-gain theorem was proposed by one of the authors in 1994. The nonlinear ISS small-gain theorem distinguishes itself from earlier small-gain theorems by providing a unified framework for internal stability and external stability of interconnected systems. Applications to a variety of control problems ranging from stabilization and robust adaptive control to decentralized or distributed control and output regulation (asymptotic tracking with disturbance rejection) have generated several novel tools for the design of robust nonlinear controllers. In the past ten years, renewed interest in large-scale nonlinear systems has motivated the further development of small-gain theorems toward a complete network small-gain theory for network stability and control. This paper provides a survey of some recent developments of the nonlinear small-gain theory and its applications in networked control systems and event-based control subject to communications and computation constraints, and gives some suggestions on this theory and future research direction.