不确定变时滞非线性随机系统的鲁棒稳定性

Robust Stability of Uncertain Nonlinear Stochastic Systems with Variable Delay

探讨了同时具有分布时滞和离散时滞的凸多面体不确定非线性随机系统的鲁棒稳定性.利用随机Lyapunov稳定性理论和自由权矩阵方法,基于参数依赖的Lyapunov-Krasovskii泛函,获得了系统的时滞相关及参数相关的鲁棒稳定性的充分条件,并以线性矩阵不等式的形式给出了系统的稳定性判据.最后用算例说明了文中方法的有效性.

This paper deals with the robust stability of polytopic-type uncertain nonlinear stochastic systems with distributed and discrete delays.In the investigation,the sufficient conditions for the delay-dependent and parameter-dependent robust stability of the systems are determined on the basis of the parameter-dependent Lyapunov-Krasovskii functional and by using the stochastic Lyapunov stability theory and the free-weighting matrix method.Then the stability criteria of the systems are proposed in the form of linear matrix inequality.A numerical example is finally presented to demonstrate the effectiveness of the proposed method.