针对具有任意切换序列的不确定线性切换系统, 提出一种鲁棒镇定切换控制律设计方法. 通过求解一组线性矩阵不等式, 计算切换系统的共同鲁棒控制Lyapunov函数, 进而构造一个双自由度的切换状态反馈控制律. 应用共同鲁棒控制Lyapunov函数性质和切换控制理论, 证明所提切换控制律的鲁棒渐近稳定性和逆最优性及共同鲁棒扇形裕度$(0.5,\mathrm{\infty })$. 最后以DC-DC升压变换器切换控制为例, 仿真验证文章方法的有效性和实用性.

A robust stabilizing switching control law is designed for linear switched systems subject to arbitrary switched rules. Common robust control Lyapunov functions (CRCLF) of the system are computed by solving a set of linear matrix inequalities, which then are used to construct a switching state feedback control law with two degrees of freedom. The results on uniformly robust asymptotical stability, inverse optimality and common robust section region $(0.5,\mathrm{\infty })$ of the obtained switching control are proved by employing the CRCLF property and the switching control theory. Finally, a simulation example of switching control of DC-DC boost converter is used to illustrate the effectiveness of the method proposed here.