Ensuring end-to-end delays meet deadlines is a key challenge in Industrial Internet of Things (IIoT), as it directly affects control performance. To reduce end-to-end delays, traditional methods focus on message scheduling under the Time Division Multiple Access (TDMA) protocol. However, with the increasing adoption of complex control algorithms in industry, neglecting task scheduling on the controller can lead to missed deadlines for control applications. This paper investigates the co-scheduling problem of messages and tasks, aiming to satisfy the end-to-end deadline constraints of all control applications in IIoT. Since the preemptive controller introduces an unknown number of task scheduling decision variables, the Early Deadline First (EDF) strategy is employed to generate task schedules. To generate message schedules aligned with task schedules, we reformulate the co-scheduling problem, making it solvable by numerical solvers. Moreover, we propose a heuristic algorithm, SECDS, for efficient scheduling in large-scale IIoT. Simulation results show the superior applicability and performance of the proposed methods compared to baseline algorithms.

This paper investigates input-output finite-time reliable static output feedback (SOF) control of a time-varying system under the influence of both input time delay and actuator failures. An actuator fault model consisting of linear and nonlinear faults is considered during the time-varying control process. The objective is to design a reliable SOF controller that can ensure input-output finite-time stability (IO-FTS) of the resulting closed-loop system. An augmented time-varying Lyapunov functional is constructed, in which some Lyapunov matrices are variable function of time t. By dividing the time interval and delay interval into equal segments, the matrix-valued functions are expressed by a linear interpolation formula. Moreover, combining with the single and double Wirtinger-based integral inequalities, delay-dependent IO-FTS conditions are derived. It is shown that the SOF control issue is solved in forms of linear matrix inequalities. In the end, the effectiveness is demonstrated by simulations.

This article discusses the issue of input-output finite-time generalized dissipative filter design for a class of discrete time-varying systems. First, an adaptive event-triggered mechanism (AETM) with an adaptive law is proposed to adjust the threshold in the AETM according to the error between the system states and the filter states. Such an AETM determines whether the measurement output should be transmitted or not, which is more effective to economize the communication resources comparing with the traditional event-triggered mechanism. Second, in view of network-induced delays, the quantization and the AETM, a time-varying filter error system (TV-FES) is modeled. Then, a new augmented time-varying Lyapunov functional containing triple sum terms is provided. Based on the new finite-sum inequality and improved reciprocally convex combination lemma, delay-dependent conditions are obtained, which can ensure the TV-FES to be input-output finite-time stable and satisfy the given generalized dissipative performance. Moreover, the recursive linear matrix inequalities are presented to obtain the desired filter gains. Finally, numerical examples demonstrate the superiority and feasibility of the proposed method in this article.