一类不确定非线性广义系统的状态反馈鲁棒H∞控制

摘要

研究一类不确定非线性广义系统的鲁棒H∞控制问题,不确定性由增益有界的摄动函数表示. 基于有广义约束条件的Hamilton-Jacobi不等式,导出系统的无控制标称系统在平衡点局部渐近稳定、是指数1的且从外部输入到控制输出的L2增益小于或等于预先设定的正数的一个充分条件. 在此基础上给出所考虑系统状态反馈鲁棒H∞控制器的一种设计方法.%This paper is concerned with the state feedback robust H∞control problem for a class of uncertain nonlinear descriptor systems. The uncertainty is described by gain bounded perturbation function on the state variables. In terms of a Hamilton-Jacobi inequality plus a generalized constraint condition,a sufficient condition is obtained for the nominal systems without control of the uncertain nonlinear descriptor systems to be locally asymptotically stable at the equilibrium point,to be of index one,and to have an L2 gain(from exogenous input to controlled output)less than or equal to a prescribed positive number. Based on this,the design method of desired state feedback robust H∞controllers of the considered systems is provided.