非线性不确定系统的时滞相关鲁棒H_∞控制

Delay-Dependent Robust H_∞ Controller Design for a Class of Nonlinear Uncertainty Time-Delay Systems with Input Delay

针对一类带有输入时滞的非线性不确定时滞系统,基于适当形式的Lyapunov泛函,利用线性矩阵不等式(Linear matrix inequation,LMI)方法,讨论了时滞相关型鲁棒H∞状态反馈控制器设计问题,其中非线性不确定性满足增益有界条件,且控制器存在的充分条件由线性矩阵不等式的形式给出。最后给出一个具体算例说明了该方法的有效性。

A delay-dependent robust H∞ state feedback control is designed for a class of nonlinear uncertainty linear time-delay systems with the input delay. The linear matrix inequalities are used based on an appropriate Lyapunov function. The nonlinear uncertain functions meet the gain bounded condition. A sufficient condition dependent on the delays of the state and input is presented for the existence of H∞ controller. The proposed controller stabilizes closed-loop uncertain systems and guarantees a prescribed H∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output. By solving a linear matrix inequation, the robust H∞ controller is obtained. Examples are given to show the effectiveness of the proposed method.