Relaxed stability conditions for Takagi-Sugeno fuzzy systems

This paper discusses conditions on stability and stabilization of continuous T-S fuzzy systems. Stability analysis is derived via a non-quadratic Lyapunov function technique and LMIs (linear matrix inequalities) formulation to obtain an efficient solution. The non-quadratic Lyapunov function is built by inference of quadratic Lyapunov function of each local model. We show that the stability condition of the open-loop T-S systems is assured under certain restrictions on the rate of change of state variables. Following a similar approach, the stabilization of closed-loop continuous T-S fuzzy systems using the well-known PDC (parallel distributed compensation) technique is investigated. The design methodology is illustrated by numerical examples.