Abstract

This work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed to force the system state onto the predefined switching surface in short time. By using Lyapunov stability theory, some novel results are obtained, and the required stability conditions are established in terms of linear matrix inequalities which can be solved by standard Matlab toolbox. Finally, the results are validated over a Chua’s circuit model, which describes the practical application of the developed results.

中文翻译：

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线性时滞系统鲁棒滑模控制的新结果

摘要

这项工作集中于具有不确定性和时变时滞的线性系统系列的滑模控制（SMC）。首先，构造一个积分开关表面以验证所考虑系统的鲁棒渐近稳定性，并扩展结果以分析混合的$ \ mathscr {H} _ {\ infty} \ big / $ Passivity性能指标。此后，开发了合适​​的SMC法则以在短时间内将系统状态强制到预定义的开关表面上。通过使用Lyapunov稳定性理论，获得了一些新颖的结果，并根据线性矩阵不等式建立了所需的稳定性条件，这可以通过标准Matlab工具箱解决。最后，通过蔡氏电路模型验证了结果，该电路模型描述了开发结果的实际应用。