Abstract
This paper is concerned with reliable state feedback control synthesis for Takagi and Sugeno (T-S) fuzzy systems with sensor multiplicative faults. By considering the influence of sensor faults on both the system states and premise variables of fuzzy controllers, a class of new convex reliable stabilization conditions are proposed for T-S fuzzy systems using the properties of fuzzy product inference engines. Furthermore, the obtained result is extended to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> reliable control case. The resulting controllers are reliable in that they provide guaranteed asymptotic stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance when all sensors are operational, as well as when some sensor experiences failures. Different from the proposed approach, the influence of sensor faults on premise variables is not considered in the existing results; then, it might not guarantee the stability and control performance for T-S fuzzy systems with premise variables dependent on the system states. A numerical example is given to illustrate the effectiveness of the proposed method.
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