一类具有凸多面体不确定性的非线性变参数系统鲁棒H_(∞)控制

Robust H_(∞)control for a class of nonlinear parameter-varying systems with polytopic uncertainty

针对具凸多面体不确定性的非线性变参数(NPV)系统,本文研究了其非线性鲁棒H_(∞)控制问题.基于Lya-punov稳定性理论和多项式平方和(SOS)方法,对该系统设计了非线性鲁棒状态反馈镇定控制器.在此基础上,进一步考虑存在外部扰动情形,给出相应的非线性鲁棒H_(∞)控制可解性条件.该条件以状态和时变参数依赖的线性矩阵不等式形式(LMIs)给出,可借助凸优化工具进行有效检验.最后,通过数值仿真验证了所得方法的有效性和优势.

This paper focuses on the nonlinear robust H_(∞)control problem for a class of nonlinear parameter-varying(NPV)systems with convex polytopic uncertainties.A nonlinear robust state feedback stabilization controller is designed based on the Lyapunov stability theory and polynomial sum of squares(SOS)method.Furthermore,by taking into consideration the external disturbances,the corresponding solvability conditions of nonlinear robust H_(∞)control are presented in the form of state-and time-varying parameter-dependent linear matrix inequalities(LMIs),which can be effectively checked with the aid of convex optimization tools.Finally,two numerical examples are given to verify the effectiveness and advantages of the proposed approach.