中文摘要：

研究了一类带有多时滞摄动的非线性切换系统的稳定性分析以及切换律的设计问题。由于时滞现象存在于大多数的切换系统中,而且时滞会使系统的性能变差,甚至破坏整个系统的稳定性。因此对于切换系统稳定性的研究,要把时滞考虑在内。首先,构造一个适当的Lyapunov-krasovskii函数（LKF）;然后,对LKF进行求导,对于该导数通过引入自由权矩阵,利用积分不等式和shur补引理以及线性矩阵不等式理论（LMI）进行推导;最后,以线性矩阵不等式的形式给出了非线性多时滞切换系统稳定性的充分条件,并给出了稳定切换律的存在条件。将单个时变时滞推广到多时变时滞,使得非线性时变时滞系统的研究更具一般性。

英文摘要：

The problem of exponential stability of uncertain switched nonlinear multiple time-delays systems is discussed.Delay phenomenon is often encountered in various switched systems,which makes the performance of the system worse,and it even disrupts the stability of the entire system.so the study of the switched system should take timedelay into account.First,we can construct a suitable Lyapunov-krasovskii function to calculate the derivative of the function.Then we can Introduce free-weighting matrix,utilize integral inequality,Shur complement lemma and linear matrix inequalities（LMI）for the derivation.At last,there is sufficient condition for the existence of a class of stabilized switching laws and derive in terms of linear matrix inequality.The single time-varying delay is extended to multiple timevarying delay,which generalizes the study of nonlinear time varying delay systems.