This article deals with the dynamic sliding mode control (SMC) problem for unmatched nonlinear parameter-varying systems. The unmatched nonlinear model refers to the systems matrices of control input and nonlinearity terms having inconsistent values and structures. A linear sliding surface function is constructed, and the resulting sliding mode dynamics is formulated into a full-order descriptor nonlinear parameter-varying system. Then, based on a parameter-dependent Lyapunov function, the synthesis procedure of the sliding manifold is derived, which guarantees the asymptotic stability of the sliding motion. Furthermore, a dynamic SMC law is proposed to enforce the resultant closed-loop system towards the sliding manifold in finite time. It is noteworthy that both the sliding surface and control law are depended on both time-varying and measurable parameters. Finally, simulation studies are provided to unfold the validity of the proposed method.

中文翻译：

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非线性变参数系统的动态滑模控制

本文处理非匹配非线性参数变化系统的动态滑模控制 (SMC) 问题。非匹配非线性模型是指具有不一致值和结构的控制输入和非线性项的系统矩阵。构建了一个线性滑面函数，并将由此产生的滑模动力学公式化为一个全阶描述符非线性参数变化系统。然后，基于参数依赖的李雅普诺夫函数，推导出滑动流形的合成过程，保证了滑动运动的渐近稳定性。此外，提出了动态 SMC 定律，以在有限时间内将合成的闭环系统推向滑动流形。值得注意的是，滑动面和控制律都取决于时变参数和可测量参数。最后，提供了仿真研究以展示所提出方法的有效性。