Stability analysis for nonlinear systems subjected to external force

This paper considers a fuzzy Lyapunov method for stability analysis of nonlinear systems subjected to external forces. The nonlinear systems under external forces can be represented by Tagagi-Sugeno (T-S) fuzzy model. In order to design a nonlinear fuzzy controller to stabilize this nonlinear system, the parallel distributed compensation (PDC). scheme is used to construct a global fuzzy logic controller. We then propose the robustness design to ensure the modeling error is bounded and some stability conditions are derived based on the controlled systems. Based on the stability criterion, the nonlinear systems with external forces are guaranteed to be stable. This control problem can be reformulated into linear matrix inequalities (LMI) problem.