一类非线性切换系统的非脆弱鲁棒H∞控制

Non-fragile Robust H_∞ Control for a Class of Switched Nonlinear Systems

针对一类不确定非线性切换系统,在控制器存在摄动的情况下,给出了非脆弱状态反馈控制器和切换律的设计方案.利用多Lyapunov函数方法,通过子系统之间的切换,使系统对所有允许的不确定性渐近稳定且具有H∞性能界.该问题可解的充分条件不依赖于Hamilton-Jacobi不等式,所提出的方法不要求任何一个子系统渐近稳定.作为应用,当单一的连续控制器难以实现时,借助混杂状态反馈策略,讨论了非切换不确定非线性的非脆弱鲁棒H∞控制问题.最后用一个例子验证了结论的有效性.

The non-fragile robust Hoo control problem is investigated for a class of uncertain switched nonlinear systems with additive gain variations. A design scheme is then given to the non-fragile feedback controllers with their switching law proposed. With the multiple Lyapunov functions used, the switching between subsystems makes the switched nonlinear systems asymptotically stable with H∞-norm bound for all allowable uncertainties. Thus, the sufficient condition solvable to the problem doesn＇t depend on the Hamilton-Jacobi inequalities. This method is suitable for the case where none of subsystems is asymptotically stable. Then, as a special application, a feedback strategy is proposed to solve the standard non-fragile robust H∞ control problem for non-switched nonlinear systems when no single continuous controller is effective. An example is given to verify the effectiveness of the proposed method.