一类非线性随机区间系统的指数稳定性分析与综合

针对一类非线性随机时变时滞区间系统,研究了其指数稳定性问题.所讨论系统中的非线性项为未知函数,且系统中每一项前均含有不确定性参数,这些参数在一定的区间内变化,利用Young不等式,特征值和范数的性质,Lyapunov第二方法以及随机微分方程的Razumikhin-type定理研究了系统的内部稳定性,给出了系统的指数稳定性的充分条件,在此基础上提出了保证系统具有指数稳定性的设计方法.

Analysis of Exponential Stability for a Class of Nonlinear Stochastic Interval Systems

For a class of nonlinear stochastic time varying delaying interval systems, its exponential stability is discussed. In the system the nonlinear terms are unknown and there are uncertain parameters contained in the antecedent of each term, which vary in a definite interval. By Young's inequality, the properties of the eigenvalues and norms, the Lyapunov Second Method and Razumikhin-type theorem of stochastic differential equations, the internal stability of the systems is analyzed, thus giving the sufficient condition of the exponential stability of the systems. A design scheme is proposed to ensure the system's exponential stability.