An LMI approach for stability analysis of nonlinear systems

This paper presents a constructive method for showing stability of nonlinear systems consisting of state-dependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or when local linear models of a nonlinear system are weighted together. Stability is shown by joining multiple local quadratic Lyapunov functions properly in the state space. The stability conditions are formulated as a linear matrix inequality (LMI) problem. Hence, these can be verified efficiently by computerized methods.