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 non-quadratic Lyapunov function technique and LMIs (Linear Matrix Inequalities) formulation to obtain an efficient solution. The nonquadratic Lyapunov function is built by inference of quadratic Lyapunov function of each local model. We show that 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, stabilization of the 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.