Conditions for uniform boundedness of parameterized discrete-time cascades

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.