The problems of relaxed quadratic stability conditions, fuzzy observer designs and H∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two suffcient LMI conditions, which guarantee the existence of the H∞ controllers basedon fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers andthe H∞ controller designs based on new observers for the T-S fuzzy systems are very practical and effcient.