Robust sampled-data stabilization of linear systems: an input delay approach

A new approach to robust sampled-data control is introduced. The system is modelled as a continuous-time one, where the control input has a piecewise-continuous delay. Sufficient linear matrix inequalities (LMIs) conditions for sampled-data state-feedback stabilization of such systems are derived via descriptor approach to time-delay systems. The only restriction on the sampling is that the distance between the sequel sampling times is not greater than some prechosen h > 0 for which the LMIs are feasible. For h → 0 the conditions coincide with the necessary and sufficient conditions for continuous-time state-feedback stabilization. Our approach is applied to two problems: sampled-data stabilization of systems with polytopic type uncertainties and to regional stabilization by sampled-data saturated state-feedback.