On the stability analysis of multiple model systems

This paper studies the global asymptotic stability of the nonlinear systems described by the multiple model approach using the Takagi-Sugeno (T-S) fuzzy modelling. New sufficient conditions for the stability of such systems are given. Stability analysis is derived via Lyapunov technique and LMIs (Linear Matrix Inequalities) formulation obtained from BMIs (Bilinear Matrix Inequalities) linearisation. Following a similar approach, sufficient conditions to guarantee the stability of T-S fuzzy systems for both T-S fuzzy controllers and T-S fuzzy observers are derived. The stabilisation of the closed loop continuous T-S fuzzy models is discussed using the well-known PDC (Parallel Distributed Compensation) technique.