转移速率部分未知的模糊广义Markov跳变系统的稳定性

Stability of Fuzzy Generalized Markov Jump Systems with Partially Unknown Transition Rate

【目的】为了得到时变时滞T-S模糊随机广义系统的稳定性与耗散性,建立一个符合现实情况的Markov跳变系统。【方法】设计一个积分型滑动曲面函数,选择一个适当的Lyapunov函数,通过线性矩阵不等式技术,得到系统的稳定性。通过运用加减项的等价处理方法,得到的结果降低了保守性。通过对滑模动力学的分析,设计一个滑模控制器。针对匹配不确定性上界未知的情况,设计一个自适应滑模控制器。【结果】在转移速率不完全已知的情况下得到系统的随机容许性条件并且系统受限于滑动曲面具有良好的稳定性和耗散性。在有限时间内系统的状态轨迹驱动到预先定义的滑动曲面并保持运动。【结论】数值实验结果表明该方法是有效的。

[Purposes]In order to obtain the stability and dissipation of T-S fuzzy stochastic singular systems with time-varying delays,a Markov jump system is established.[Methods]An integral sliding surface function is designed and an appropriate Lyapunov function is selected.The stability of the system is obtained by linear matrix inequality(LMI)technique.By using the equivalent treatment method of addition and subtraction,the result reduces the conservatism.Through the analysis of sliding mode dynamics,a sliding mode controller is designed.An adaptive sliding mode controller is designed for the case that the upper bound of matching uncertainty is unknown.[Findings]When the transfer rate is not fully known,the stochastic admissibility condition of the system is obtained,and the system is constrained by the sliding surface,which has good stability and dissipation.In a finite time,the state trajectory of the system is driven to a predefined sliding surface and keeps moving.[Conclusions]Numerical experiments show that the method is effective.