STABILITY OP TIME VARYING NONLINEAR DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

摘要

The stability of Time Varying Nonlinear Difference Equations with Continuous Time is here addressed. Lyapunov theorems are built up for the absolute stability of the origin. Among many other cases such as economic models, these systems are encountered as input output linearizable nonlinear delay systems internal dynamics. Indeed, when a nonlinear delay system admits full delay relative degree, the output and its derivatives until a suitable order can be driven to zero by a suitable control law, while the system variables depend on such output and derivatives and on their past values, on continuous time. This paper shows a Lyapunov methodology to check such internal dynamics. An example is reported of linearizable nonlinear delay system, which has a stable internal dynamics, proved by the methodology here shown.