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Robust H_∞ control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems

机译：Takagi-Sugeno一般不确定模糊系统的鲁棒H_∞控制分析与综合

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In this paper robust H_∞ control for Takagi-Sugeno general uncertain fuzzy systems where uncertainties come into all the system matrices is considered. The main result is to establish equivalent relationships between quadratic stability and quadratic stability with H_∞ disturbance attenuation γ of general uncertain fuzzy systems and H_∞ control for fuzzy systems without uncertainty. These relationships imply that quadratically stabilizing controllers and quadratically stabilizing controllers with H_∞ disturbance attenuation γ for general uncertain fuzzy systems can be obtained by designing H_∞ controllers for fuzzy systems without uncertainties. We first give sufficient conditions for the H_∞ norm being less than a given number. We then consider a general H_∞ problem with output feedback controllers, and give a design method of H_∞ controllers and sufficient conditions which guarantee the required H_∞ performance of the closed-loop system. This design method can be applied to quadratic stabilizing controllers and quadratic stabilizing controllers with H_∞ disturbance attenuation γ for general uncertain fuzzy systems. Next we analyze quadratic stability and quadratic stability with H_∞ disturbance attenuation γ of general uncertain fuzzy systems and establish equivalent relationships to H_∞ control of fuzzy systems without uncertainties. Based on these relationships, we design robust controllers for uncertain fuzzy systems. Finally, examples are given to illustrate the theory.
机译：本文考虑了不确定性进入所有系统矩阵的Takagi-Sugeno广义不确定模糊系统的鲁棒H_∞控制。主要结果是建立一般不确定模糊系统的H_∞扰动衰减γ和没有不确定性模糊系统的H_∞控制的二次稳定性和二次稳定性之间的等价关系。这些关系表明，通过为不确定系统设计不确定性的H_∞控制器，可以获得一般不确定模糊系统的H_∞干扰衰减为γ的二次稳定控制器和具有H_∞干扰的二次稳定控制器。我们首先给出H_∞范数小于给定数的充分条件。然后，我们考虑了带有输出反馈控制器的一般H_∞问题，并给出了H_∞控制器的设计方法和充分的条件，这些条件保证了闭环系统所需的H_∞性能。该设计方法可应用于一般不确定模糊系统的二次稳定控制器和具有H_∞干扰衰减γ的二次稳定控制器。接下来，我们分析了一般不确定模糊系统的H_∞扰动衰减γ的二次稳定性和二次稳定性，并建立了具有不确定性的模糊系统H_∞控制的等价关系。基于这些关系，我们为不确定的模糊系统设计了鲁棒的控制器。最后，通过实例说明了该理论。

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