SIAM Journal on Control and Optimization, Vol.42, No.3, 936-965, 2003
A converse Lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization
Lyapunov-like characterizations for the concepts of nonuniformin time robust global asymptotic stability and input-to-state stability for time-varying systems are established. The main result of our work enables us to derive (1) necessary and sufficient conditions for feedback stabilization for affine in the control systems and (2) sufficient conditions for the propagation of the input-to-state stability property through integrators.
Keywords:nonuniform in time asymptotic stability;input-to-state stability;Lyapunov functions;feedback stabilization