A new class of strict Lyapunov functions for nonlinear time-varying systems

This paper focuses on strict Lyapunov functions of nonlinear time-varying systems using homogeneity-based methods. The concept of homogeneous auxiliary system is introduced. Based on the auxiliary system, a new class of strict Lyapunov functions is established. Sufficient conditions of uniform asymptotic stability are provided under the homogeneous framework. The results are extended to deal with robustness problems. It is shown that the nonlinear time-varying systems remain stable in the presence of higher order perturbing terms.