New Generalized Stability Conditions for Takagi-Sugeno Fuzzy Time-Delay Systems

In this paper, we consider new generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy time-delay systems. In the literature, both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been obtained. However, those conditions are rather conservative and do not guarantee wide stability regions. This is also true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. Here we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. In the auxiliary system, we have some arbitrary matrices that generalize a system representation. In fact, this auxiliary system generalizes not only the system representation but also delay-dependent stability conditions. Delay-dependent conditions we obtain here depend on the upper bound of time-delay and are given in linear matrix inequalities (LMI´s). Then, we compare our generalized delay-dependent stability condition with other stability conditions in the literature, and show that our condition is a generalized one. Next, we consider the stabilization problem. Based on our generalized delay-dependent stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be stable. Finally, we give a simple example that illustrates our result