中文摘要：

本文研究了一类不确定线性切换系统的二次鲁棒稳定性问题．首先利用矩阵集的严格完备性设计切换律，导出了二次鲁棒稳定的充分条件。同时得到了在任意切换策略下，当矩阵集的所有矩阵为负定时保证切换系统二次鲁棒稳定性。在适当的假设下，这些条件可以表示为矩阵不等式。最后，用数值例子对所得结果加以阐明，说明了文中结果的正确性。

英文摘要：

This paper investigates the quadratic robust stability problem for a class of switched linear systems with uncertainties. We show that the strict completeness of certain family of matrices guarantees quadratic robust stability. A switching law is also designed according to the strict completeness. When all matrices of this family are negative definite, quadratic robust stability under arbitrary switching laws is obtained. Under appropriate assumptions, the conditions are expressed in the LMIs form. A numerical example is given to illustrate the effectiveness of the results.