不确定非线性切换系统的鲁棒H∞控制

讨论了一类不确定非线性切换系统的鲁棒H∞控制问题．首先,基于多Lyapunov函数方法,设计状态反馈控制器以及切换律,使得对于所有允许的不确定性．相应的闭环系统渐近稳定又具有指定的L2-增益．该问题可解的充分条件以一组含有纯量函数的偏微分不等式形式给出,此偏微分不等式较一般Hamilton-Jacobi不等式更具可解性．所提出的方法不要求任何一个子系统渐近稳定．接着作为应用,借助混杂状态反馈策略讨论了非切换不确定非线性系统的鲁棒H∞控制问题．最后通过一个简单例子说明了控制设计方法的可行性．

Robust H-infinity control for uncertain switched nonlinear systems

The robust H-infinity control problem for uncertain switched nonlinear systems is discussed in this paper. First, based on multiple Lyapunov function technique, for all admissible uncertainties, the state feedback controllers for each subsystem and switching laws to guarantee both internal stability of the resulting closed-loop systems and prescribed L2-gain from disturbance input to the controlled output are designed respectively. The sufficient condition for the problem to be solvable is also derived in terms of partial differential inequalities with scale functions, which are more feasible to be solved than general Hamilton-Jacobi inequalities. This method is suitable for the case where none of subsystems is asymptotically stable. Then, as an application, a hybrid state feedback technique to solve the robust H-infinity control problem for non-switched nonlinear systems is presented. Finally, a simple example is given to illustrate the proposed method.