一类不确定时滞非线性系统的H∞鲁棒镇定

H-infinity robust stabilization for a class of uncertain time-delay nonlinear systems

利用混杂状态反馈策略研究一类不确定时滞非线性系统的鲁棒H∞镇定问题。首先,当控制器增益矩阵均已知时,利用单Lyapunov函数法和凸组合技术,给出了闭环非线性切换系统具有鲁棒H∞性能的充分条件并设计出相应切换律。然后,当控制器增益矩阵均未知时,利用多Lyapunov函数法,设计了控制器及相应的切换策略,使闭环非线性切换系统是鲁棒H∞渐近稳定的。

The problem of H infinity robust stabilization for a class of uncertain time-delay nonlinear systems is investigated by using a hybrid state feedback method. First, when the gain matrices of controllers are all known, by using the single Lyapunov function method and convex combination technique, the sufficient condi tions of closed-loop switched nonlinear systems with robust H infinity performance are derived and the corre sponding switching laws are designed. Then, when the gain matrices of controllers are unknown, by employing muhi-Lyapunov function method, the controllers and the switching laws are designed, which guarantees that the closed loop switched nonlinear system is robust H infinity asymptotically stable.