The paper considers sliding manifold design for higher-order sliding mode (HOSM) in linear systems. In this case, the sliding manifold must meet two requirements: to achieve the desired dynamics in HOSM and to provide the appropriate relative degree of the sliding variable depending on the SM order. It is shown that in the case of single-input systems, a unique sliding manifold can be determined that satisfies these two requirements, whereas in multi-input case, such a manifold exists only in systems satisfying specific structural constraints. Theoretically obtained results are validated through numerical examples and illustrated by digital simulations.

中文翻译：

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线性系统高阶滑模控制的滑动流形设计

本文考虑了线性系统中高阶滑模 (HOSM) 的滑动流形设计。在这种情况下，滑动流形必须满足两个要求：在 HOSM 中实现所需的动力学和根据 SM 阶数提供适当的滑动变量相对程度。结果表明，在单输入系统的情况下，可以确定满足这两个要求的唯一滑动流形，而在多输入情况下，这种流形只存在于满足特定结构约束的系统中。理论上获得的结果通过数值例子进行验证，并通过数字模拟进行说明。