An LMI approach to stability for linear time-varying system with nonlinear perturbation on time scales

Abstract

We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results. © 2011 Kanit Mukdasai and Piyapong Niamsup.