ABSTRACT
This chapter introduces a class of models for discrete-time dynamical systems. Discrete-time dynamical systems play an important role in modelling many real-world processes, both engineered systems and physical systems present in nature.
Arguably one prominent reason to consider discrete-time control systems is to cope with digital and sampled-data control applications. From a theoretical point of view, discrete-time control systems can be modeled by difference equations with inputs. This chapter briefly discusses such models. It provides sufficient conditions in terms of Lyapunov functions for stability, boundedness, invariance, safety, and reachability specifications. Lyapunov and barrier functions are unified to provide sufficient conditions for stability with safety requirements.
