NEW CRITERION OF STABILITY FOR TIME-VARYING DYNAMICAL SYSTEMS: APPLICATION TO SPRING-MASS-DAMPER MODEL

In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model.