Controllability and Observability of Input /Output Delayed Discrete Systems

This paper proposes the study of network-delayed systems controllability and observability. Since the controllability and observability are the first conditions we impose in control practice, we study if a controllable/observable non-delayed system can loose those properties if we augment the model with pure input-output delays due to network control architecture. We started our approach with a classical discrete-time multi-input/output linear system with non-equal network-induced delays on command signals (inputs) and measures (outputs). We will prove that if the initial (non-delayed) system is controllable/observable, the new network-delayed system is controllable/observable despite the delay values in each input/output channel. This general result ensures further implementation of model-based predictive control strategies based on state observers, especially LQG/LTR, H₂ or loop-shaping H_infin methods for networked control systems