Stabilization of linear systems with aperiodic sampled-data control

This paper is concerned with the sampled-data stabilization problem for a class of linear systems. Different from the input-delay approach that has been widely used in analyzing the stabilization problem of sampled-data systems, an extended form of the celebrated Halanay inequality is developed for sampled-data systems so as to study the stabilization problem of linear systems under aperiodic sampled-data control. Based on the extended Halanay inequality, the stabilization problem is solved for linear sampled-data systems, where it is required that the gain should be strictly less than the decay rate and then the upper bound of the sampling intervals can be estimated. In order to enlarge the upper bound of the sampling intervals, a further extension of the developed Halanay inequality is made. Then some new conditions are derived to ensure the exponential stability of linear sampleddata systems, where the upper bound of the sampling intervals is allowed to violate the condition of the Halanay inequality. Subsequently, the obtained results are applied to deal with the consensus problem of linear multi-agent systems.