Discrete-Time Trajectory-Based Stabilization Approach Using Interval Observer

We provide a discrete-time vector valued analog of recently developed continuous-time trajectory-based estimates. We use it to provide a discrete-time version of Halanay’s inequality. We combine the results with interval observers to prove exponential stability properties for discrete-time linear systems with uncertainties whose arbitrarily long input delays are compensated for by reduction model controls, and a robust global exponential stability result for observers for discrete-time linear systems.