Abstract
This paper presents stability analysis for a class of nonlinear systems and a design method of fuzzy controllers to stabilize the nonlinear systems. First, a stability condition is introduced in terms of Lyapunov stability theory. Next, stability conditions for a class of uncertain systems are given from the viewpoints of quadratic stabilization, H∞ control theory and Linear Matrix Inequalities. Furthermore, some stability conditions are derived for a generalized class of uncertain systems. The derived stability conditions for a generalized class are used to analyze stability of nonlinear control systems designed via parallel distributed compensation. Some important issues for the stability analysis are remarked. Finally, we demonstrates controller design examples. It is pointed out in the examples that a conservative result of stability analysis can be avoided by introducing the singular value decomposition.
