Robust Exponential Stability for a Class of Nonlinear Uncertain Systems

摘要

Exponential stability analysis via the parameter and state dependent Lyapunov functions method is extended to a class of nonlinear polynomial systems. By introducing some slack matrices, we succeed in separating the product of the system matrices and the Lyapunov matrices. Less conservative sufficient conditions are formulated in terms of state dependent matrix inequalities. These conditions can be verified by the technique of sum of squares(SOS) approach. A numerical simulation example shows the effectiveness of the proposed approach.