It is well known that the general stability condition for a T-S fuzzy system is AiT P + PAi < O (for continuous systems) or AiT PAi - P < O (for discrete systems), i=1,2,...,r, where r is the number of system's rules. If rules' number r of the fuzzy system is large, the problem for finding the common P to satisfy r inequalities is not easy, even 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 fied, have zero fired grade membership values. Therefore it is not necessary to consider them into the system's stability condition. This paper will investigate the problem to relax 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.
|Number of pages||6|
|State||Published - 2001|
|Event||Joint 9th IFSA World Congress and 20th NAFIPS International Conference - Vancouver, BC, Canada|
Duration: 25 Jul 2001 → 28 Jul 2001
|Conference||Joint 9th IFSA World Congress and 20th NAFIPS International Conference|
|Period||25/07/01 → 28/07/01|