Exponential stability analysis of nonlinear systems using LMIs

This paper presents a constructive method for showing exponential stability of autonomous nonlinear systems consisting of state-dependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or is the result of an exact or approximative description of an arbitrary nonlinear vector field. Stability is shown by joining multiple local Lyapunov functions properly in the state-space. The overall Lyapunov function, consisting of the local ones, are allowed to be discontinuous at the states where the trajectory passes from one local region to another. By using local quadratic Lyapunov functions the stability conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently by computerized methods.