Sampled-Data Control for Linear Systems on Hybrid Time Domains

Sampled-data control has been broadly used to stabilize various systems due to its advantages in reducing communication burdens, where the sampling instances are usually determined by a pre-designed sampling protocol. However, the methods of sampled-data control for continuous-time systems are no longer applicable to time-scale systems mainly because that the discontinuity of time domains may result in inaccessible information at pre-designed sampling times. As a result, a new time scale type sampled-data control protocol (TTSDCP) is provided to stabilize linear systems on time scales, where a backward-jump-like function is introduced to ensure that all sampling times are located on time scales. Based on the proposed TTSDCP, and the generalized Gronwall-Lemma, the exponential stability is considered for time-scale-type linear systems under sampled-data protocol. Finally, a numerical example is given to verify the effectiveness of the obtained results.