An LMI approach to stability for linear time-varying system with nonlinear perturbation on time scales (Q554955)

Summary: We consider Lyapunov's stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, \(\psi\)-uniform stability, and \(h\)-stability for linear time-varying system with nonlinear perturbations 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.