Sampled-Data Control for Time-Scale-Type Systems Under Denial-of-Service Attacks

This article tackles the sampled-data control issue for a class of time-scale-type systems (TSTSs) subject to denial-of-service (DoS) attacks. A novel sampled-data control protocol, that incorporate the backward-jump-like operator (BJLO), is proposed to ensure compatibility with the discontinuity of time scales. Furthermore, a generalized Halanay-like inequality (GHLI) is proposed to address the effects of time scale discontinuities and DoS attacks on sampling intervals. Compared with the common Halanay inequality (CHI) used in continuous-time sampled-data systems, the GHLI accommodates TSTSs and permits some sampling intervals that exceed the constraints of the CHI. By leveraging the GHLI and the proposed sampled-data control protocol, the exponential stability criterion is derived for TSTSs under DoS attacks. This article culminates with two simulation examples and the micro-grid case study conducted to validate the proposed results.