Robust H∞ control analysis and synthesis for Takagi–Sugeno general uncertain fuzzy systems

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.