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A sliding mode control for linear systems with input and state delays

This paper describes a variable structure control for linear multi-input delayed systems. The first part develops some new delay-dependent stability criterion to be used further in the control synthesis. On this basis, two different discontinuous unit controllers ensuring the global asymptotic stability are developed. The original contribution is to allow delayed inputs; the calculation of admissible upper bounds for the delay is provided by using an appropriate Lyapunov-Krasovskii functional. A final example illustrates the study.