一类连续级联系统的全局一致稳定性

Globally Uniform Stability of a Class of Continuous Cascaded Systems

针对一类非线性连续级联系统,利用齐次系统的齐次性质给出了其全局一致稳定性分析结果.假设级联系统中的驱动子系统和被驱动子系统分别满足全局一致渐近稳定且满足一定的齐次度,若级联项也满足一给定齐次不等式,则整个非线性级联系统为全局一致渐近稳定的.若驱动子系统和被驱动子系统都具有负的齐次度,则该非线性级联系统为全局一致有限时间稳定的.与传统的ISS假设或级联项增长假设相比,文中方法所给的齐次不等式条件更容易验证.且文中方法不仅适用于Lipschitz连续的系统,而且适用于非Lipschitz连续的系统.两个例子验证了该方法的有效性.

Globally uniform stability is obtained for a class of nonlinear continuous cascaded systems by using homogeneous properties of homogeneous systems. It is assumed that the driving subsystem and the driven subsystem have globally uniformly asymptotical stability and have certain degrees of homogeneity. If the cascaded term also satisfies a homogeneous inequality, then the cascaded system has globally uniformly asymptotical stability. Furthermore, if both the driving subsystem and the driven subsystem have the negative degrees of homogeneity, the cascaded system is globally uniformly finite-time stable. Compared with the conventional ISS assumption or the growth assumption of the cascaded term, the homogeneous inequality assumption of the cascaded term is easier to verify. Furthermore, the proposed method can be applied not only to the Lipschitz continuous systems but also to the non-Lipschitz continuous systems. Two examples ave given to verify the effectiveness of the method.