New stabilisation schemes for discrete delay systems with uncertain non-linear perturbations

New _∞ controller design schemes are provided for a class of discrete-time systems with uncertain non-linear perturbations. The class includes both systems with time-varying delays and systems without delay. One design scheme is generated by state-feedback and the other scheme is based on proportional-summation-difference (PSD) feedback. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed and a new parametrised characterisation is established in terms of feasibility-testing of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the theoretical developments.