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

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

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New ℋ 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.

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