具有受限转移率的跳变系统L_2-L_∞模糊控制

L_2-L_∞ fuzzy control of jump systems with bounded transition probabilities

讨论了一类含不确定转移率的非线性Markov跳变系统的L2-L∞模糊控制问题。系统模态间转移概率所包含的不确定性是未知且有界的。通过Takagi-Sugeno模型模糊建模,获取了整个闭环模糊动态方程。基于L2-L∞模糊控制理论,提出了使得系统随机稳定且满足一定输入输出L2-L∞特性的模态依赖的模糊控制器存在条件。利用构造的Lyapunov-Krasovskii函数,结合线性矩阵不等式技术,给出了鲁棒L2-L∞模糊控制器的设计方法,并将其设计转化为一个优化问题。仿真示例说明了设计方法的有效性。

The L2-L∞ fuzzy control problem of a class of nonlinear Markov jump systems（MJSs） with uncertain transition jump rates is studied.The uncertain transition jump rates are assumed unknown but bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamic equalities are constructed through selected membership functions.Based on the L2-L∞ fuzzy control theory,the sufficient condition for the existence of mode-dependent fuzzy controller is given so that the fuzzy MJSs are stochastically stable for all admissible uncertainties and satisfy the given L2-L∞ control index.By using the constructed Lyapunov-Krasovskii function and applying linear matrix inequality techniques,the design scheme of the robust L2-L∞ fuzzy controller is derived and described as an optimization one.Simulation results demonstrate the validity of the proposed approach.