非线性时变系统的部分指数稳定性分析

Partial exponential stability analysis of nonlinear time-varying systems

讨论了非线性时变系统平凡解的部分指数稳定性和全局部分指数稳定性。分别利用数量与向量Lyapunov函数并结合数量与向量比较原理,得到了保证系统平凡解部分指数稳定和全局部分指数稳定的一系列充分条件。作为特殊情形,对于一类定常拟线性系统,在一定的条件下,若其对应的线性系统的平凡解是部分渐近稳定的,利用二次型Lyapunov函数得到了保证拟线性系统的平凡解是全局部分指数稳定的一个代数判据,这些结果在实际应用中具有一定的指导意义。最后用两个数值例子对所得主要结果加以阐明。

The partial exponential stability and globally partial exponential stability are studied for nonlinear time-varying systems. A set of sufficient conditions for partial exponential stability and globally partial exponential stability of the null solution of nonlinear time-varying systems are established via scalar and vector Lyapunov functions and scalar and vector comparison technique. In the special case, under reasonable conditions, an algebraic criterion for globally partial exponential stability of the null solution for a class of quasi-linear system is also derived by using quadratic Lyapunov functions where the null solution of its corresponding linear systems is partially asymptotically stable. The results presented will be instructive to some practical applications. Finally, two numerical examples are presented to illustrate the effectiveness of these theoretical results.