基于T-S模糊的Delta算子时滞系统的H∞控制

H_∞ Control for Delta Operator Systems With Time-delay and T-S Fuzzy

针对T-S模糊Delta算子时滞系统的H_∞控制问题。假设系统含有范数有界不确定性和时滞现象,设计了一个具有H_∞性能的状态反馈控制器,使得闭环系统是渐近稳定的。运用Lyapunov稳定性理论,将该控制问题化为线性不等式矩阵问题,由此给出满足H_∞性能指标γ的状态反馈控制律Kj(j=1,2,…,p)的存在条件和设计方法,然后通过Matlab工具箱中的LMI解得状态反馈控制器Kj。最后通过数值计算,验证了该方法的可行性。

The H_∞control problem of T-S fuzzy Delta operator time-delay system is studied in this paper.Assuming that the system contains norm-bounded uncertainties and time-delays,a state feedback controller is proposed to make the closed-loop system asymptotically stable.By using Lyapunov stability theory,the control problem is transformed into a linear inequality matrix problem,and the existence condition and design method of state feedback control law are given.Then the state feedback controller is solved by LMI in Matlab toolbox.Finally,the feasibility of this method is verified by numerical calculation.