Relaxed stability conditions for T-S fuzzy systems

It is well known that the general stability condition for a T-S (Takagi-Sugeno) fuzzy system is A_l^T P + PA_l <0 (for continuous systems) or A_l^T PA _l-P <0 (for discrete systems), i=1, 2,...r, where r is the number of system´s rules. If the rules number r of the fuzzy system is large, the problem of finding the common P to satisfy r inequalities is not easy, even if linear matrix inequality (LMI) is used. However, in practical, when inputs are singletons, the number of the fired rules at the instance is always very less than (at most equal to) r. Those rules, which are not fired, have zero fired grade membership values. Therefore it is not necessary to consider them in the system´s stability condition. The paper investigates the problem of relaxing the stability condition, that is, the common P only needs to satisfy h inequalities instead of r inequalities, where h (⩽ r) is the number of the fired rules by each input sets. Thus, the new and relaxed stability condition is established