Robust stabilisation of a state delayed system

In the paper, the authors present a method for stabilising uncertain time-delay systems. The systems under consideration are described by linear state delayed equations whose coefficient matrices contain norm-bounded time-varying elements. Using some matching conditions, they can take time-varying elements and re-form the equation into a linear state delayed equation with disturbances. They then apply a linear transformation technique to reduce the uncertain systems to those where nominal systems are delay-free. Consequently, they can derive a suitable controller for the perturbed systems, and will prove that the controller can robustly stabilise the closed-loop systems against perturbation. Finally, a control system design for the two-tank chemical reactor with a delayed repeat cycle is illustrated to show the applicability of the proposed method