一类含扰动的非线性切换系统稳定性分析

Stability analysis for a class of switched nonlinear systems with perturbations

首先在非零扰动情况下,利用平均滞留时间的方法给出保证切换系统一致有界或一致终极有界的条件以及最终边界.当切换系统中含有不稳定子系统时,证明了当切换规则满足一定条件时,仍可保证切换系统是有界的.然后在零扰动情况下,给出了扰动非线性切换系统稳定的充分条件.最后通过仿真算例说明了所得结果的有效性.

Under the condition of non-vanishing perturbation, sufficient conditions for guaranting the uniformly boundness and uniformly ultimate boundness of system＇s solution are derived. When the system is composed of unstable subsystems and stable subsystems, it is proved that if the activation time of stable subsystems is relatively large compared with that of unstable subsystems, then the boundness is guaranteed. Under the condition of vanishing perturbation, a sufficient condition of the stability of the system is derived. Finally, the simulation results show that the methods proposed is effective.