A homogeneity property of discrete‐time systems: Stability and convergence rates

A new definition of homogeneity for discrete‐time systems is introduced. As in the continuous‐time case, the property can be verified algebraically in the transition map of the system, and it implies that a dilation of the initial conditions leads to a scaling of the trajectory. Stability properties and convergence rates of the system's solutions can be established by considering only the homogeneity degree. The existence of homogeneous Lyapunov and Lyapunov‐like functions is proven.