Robust stability bounds for networked controlled systems with unknown, bounded and varying delays

A robust control-oriented modelling approach for networked controlled systems (NCS) with uncertain, varying, bounded transmission delays and asynchronous discrete-time control laws is presented. The resulting model is then used for the derivation of sufficient conditions for the robust stability of NCSs and the computation of the maximum allowable delay (constrained within one sampling period) that the closed-loop system can tolerate given a pre-selected set of stabilising gains for the nominally delayed system. The derived stability conditions can be used for both open-loop stable and unstable systems and are numerically simple to use because they rely on singular-value calculations and the solution of a standard discrete Lyapunov equation. The impact of certain designer choices (such as sampling period, nominal delay and tuning parameters appearing in the stability conditions) on the delay range is also investigated. Simulation studies are used to investigate the efficiency of the derived robust stability bound.