Relaxed stability conditions for Takagi-Sugeno fuzzy systems

Mohammed Chadli (1) , Didier Maquin (1) , José Ragot (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

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.

Domains: Automatic

Mohammed Chadli, Didier Maquin, José Ragot. Relaxed stability conditions for Takagi-Sugeno fuzzy systems. IEEE International Conference on Systems, Man, and Cybernetics, SMC'2000, Oct 2000, Nashville, United States. pp.3514-3519, ⟨10.1109/ICSMC.2000.886553⟩. ⟨hal-00201428⟩