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In this article, we propose an improved delayed output-feedback sliding mode control of a fuzzy system with arbitrary order. A new time-delay estimator is designed for approximating the output derivatives in sliding surface, which has appealing noise attenuation capability. Then, such estimator is embedded in the feedback loops, which results in a static delayed output-feedback sliding surface. On this basis, the sliding mode control law depending on consecutive measurements is used to stabilize the fuzzy system subject to estimation biases and measurement noises. Different from the existing publications, the estimator and controller parameters are codesigned by genetic algorithm to make a tradeoff among multiple objectives: the closed-loop stability, noise attenuation, and estimation accuracy. The resulting design method is demonstrated by two examples: a mass-spring-damper system and a single-link rigid robot system.
Xu et al. (Sun,) studied this question.
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