非线性广义离散区间系统的鲁棒非脆弱H_∞控制

Robust and Non-fragile H_∞ Control for Nonlinear Descriptor Discrete Interval Systems

研究一类含有非线性扰动的广义离散区间系统的鲁棒非脆弱H∞控制问题,所研究的非线性扰动满足Lipschitz条件.首先,利用Lyapunov函数理论,研究不确定非线性广义系统的鲁棒H∞控制问题;其次,以线性矩阵不等式(LMI)形式,给出了系统鲁棒非脆弱H∞控制器存在的充分条件,使得对于所有容许不确定性,闭环系统都允许且H∞性能指标满足给定上界.同时,给出状态反馈控制器的设计方法;最后,用数值例子表明了所提出方法的有效性.

The problem of robust and non-fragile H∞ control for a class of descriptor discrete interval systems with nonlinear disturbance was studied,where the nonlinear disturbance satisfies the Lipschitz condition.First of all,based on the theory of Lyapunov function,the robust H∞ control problem of the uncertain nonlinear descriptor system was described;Secondly,a sufficient condition for the existence of robust and non-fragile H∞ controller was given by linear matrix inequality approach,which guarantees that the resulting closedloop descriptor system is admissible and satisfies a prescribed H∞ normbounded constrain for all admissible uncertainties.Meanwhile,the design method of the state feedback controller was proposed.Finally,numerical simulation results indicated the effectiveness of the developed method.