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

In this paper robust H-infinity 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-infinity disturbance attenuation gamma of general uncertain fuzzy systems and H-infinity control for fuzzy systems without uncertainty. These relationships imply that quadratically stabilizing controllers and quadratically stabilizing controllers with H-infinity disturbance attenuation gamma for general uncertain fuzzy systems can be obtained by designing H-infinity controllers for fuzzy systems without uncertainties. We first give sufficient conditions for the H-infinity norm being less than a given number. We then consider a general H-infinity problem with output feedback controllers, and give a design method of H-infinity controllers and sufficient conditions which guarantee the required H infinity performance of the closed-loop system. This design method can be applied to quadratic stabilizing controllers and quadratic stabilizing controllers with H-infinity disturbance attenuation gamma for general uncertain fuzzy systems. Next we analyze quadratic stability and quadratic stability with H-infinity disturbance attenuation gamma of general uncertain fuzzy systems and establish equivalent relationships to H-infinity 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. (C) 2006 Elsevier B.V. All rights reserved.