Stabilization of singularly perturbed fuzzy systems

This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H^∞ control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all ε∈(0,ε^*) and the upper bound ε^* can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H^∞ control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval ε∈[ε_,ε~]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.