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中文摘要：
针对一类全矩阵形式的非线性系统,研究其全局稳定性及有限时间镇定问题.首先,全矩阵形式非线性系统被分成上三角形式和下三角形式非线性系统的加和,并针对下三角形式非线性系统,利用加幂积分方法,自上而下地设计系统的全局稳定控制器;其次,在上面控制器作用下,证明全矩阵形式系统在一个给定领域内是局部渐近稳定的;最后,运用自下而上的顺序,一种嵌套饱和方法被用到上述控制器中,通过调节饱和度,使得闭环系统全局渐近稳定.此外,在适当的条件下,可以得到全矩阵形式非线性系统的全局有限时间稳定性.
英文摘要：
In this paper,the problems of global asymptotic and finite-time stability of a class of nonlinear systems are considered.The control law is designed in the following three steps：First,the full matrix form nonlinear system is divided into a lower-triangular form plus a upper-triangular form.And for the lower-triangular systems,the generalized adding a power integrator technique is used to design the global stabilization controller from top to bottom.Next,we proof that the whole system is locally asymptotically stabile in a given region under the above controller.Finally,a series of nested saturations are imposed on the above controller.And by adjusting the saturation level,the global asymptotic stability of the closed-loop systems is ensured.In addition,we can also obtain the global finite-time stability of the whole nonlinear system under appropriate conditions.
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