Controllability and Observability of Linear Discrete-Time Systems with Network Induced Variable Delay

This paper studies the controllability and observability of discrete-time systems with network-induced variable delays. Since controllability and observability are structural properties of systems, which are first checked before control design, we study if a controllable (resp. observable) non-delayed system can loose these properties if we augment the model with particular pure input-output variable delays caused by a situation of overload in the networked control architecture. We start our approach with a discrete-time multivariable linear time-invariant system with non-equal network-induced delays on control signals (inputs) and measures (outputs). The considered delays may only remain constant or increase with unitary increments. We prove that if a non-delayed system is controllable (resp. observable), then the network-delayed system is controllable (resp. observable) despite the monotonicallyincreasing delay values in each input/output channel. This general powerful result ensures further implementation of model-based predictive control strategies based on state observers methods for the considered model of networked control systems.