Periodically Intermittent Control of Hybrid Stochastic Delay Systems With Asynchronous Switching by Sampled-Data Feedback

In this article, the design of periodically intermittent controller (PIC) using sampled-data feedback for hybrid stochastic delay systems (SDSs) with asynchronous switching is studied. This article can be divided into two parts. First, the design of sampled-data-based controllers (SDBCs) via lifting technique (LT) for SDSs with asynchronous switching is discussed. Then, for SDSs with SDBCs, this article takes a further step to design sampled-data-based PIC, which is also based on the LT. For SDBCs design, there are two techniques: 1) the LT and 2) the input time delay method (ITDM). In the case of linear systems, the LT yields better results. However, for nonlinear SDSs modeled by unsolvable equations, there is no prior research on the application of the LT. Thus, in the first part of this article, the LT for nonlinear SDSs with asynchronous switching is generalized. Moreover, comparisons are presented between the LT and the ITDM, showing the superiority of the LT. In the second part, focusing on the design of PICs, some novel mathematical techniques are introduced. This article utilizes the auxiliary system method based on the LT, which is capable of addressing cases where $T< \delta$, with $T$ and $\delta$ denoting the control frame and sampling interval, respectively. Finally, one numerical example and one comparison are provided to show the process of controller design and the superiority of the generalized LT.