随机耗散系统理论为随机稳定性提供了新的分析工具, 本课题则致力于从两个方面发展这一理论成果. 一方面, 采用确定系统中的行为动态系统方法, 并借助于随机Barbalat引理, 为随机受控系统的耗散性与稳定性构造理论框架, 主要研究课题包括: 提出多种条件耗散性和输入状态稳定的定义, 并建立彼此间的关系; 将条件耗散与稳定性用于关联系统的耗散性与稳定性分析; 将条件耗散与逆Lyapunov方法结合解决随机控制问题. 另一方面, 给出随机切换系统稳定性分析和随机切换控制理论, 有五个主要的研究方向: 随机切换系统的解的构造, 随机切换系统稳定性分析, 利用随机鲁棒稳定性分析随机切换系统的一致稳定性, 基于凸组合的随机切换控制, 具有时滞的随机切换系统. 研究的问题多为随机非线性控制中公开的问题, 将推广较多的经典理论, 难度大, 具有一定的挑战性.

The theory of stochastic dissipative systems provides new analysis tools for stochastic stability. This project will take great efforts to further improve this theory in two directions. First, by adopting the viewpoint of behavioral dynamical systems and by the aid of stochastic Barbalat lemma, a framework of stability and dissipativity for stochastic control system is constructed: Many forms of conditional dissipativity and input-to-state stability as well as some relations among them are presented; Properties of conditional dissipativity are used to dissipativity analysis for interconnected systems; Stochastic controller design is dealt with by combing conditional dissipativity with inverse Lyapunov method. Second, stochastic switched systems and stochastic switching control are considered: construction of solution to switched system, stability analysis to switched systems, uniform stability and stochastic robust stability, stochastic switching control based on convex combination and tochastic switched systems with time-delays. Most of the researched issues are open problems with great challenging, which are the extensions of many classical results.