On uniform boundedness of parameterized discrete-time systems with decaying inputs: applications to cascades

Abstract

A framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been established recently. Within this framework naturally arises the need to investigate stability properties of parameterized discrete-time systems. Further results that guarantee appropriate stability of the parameterized family of discrete-time systems that is used within this framework have been also established for systems with cascaded structure. A fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade. However, this is difficult to check in general. In this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check. These results further contribute to the toolbox for controller design of sampled-data nonlinear systems via their approximate discrete-time models.