Event‐triggered control via impulses for exponential stabilization of discrete‐time delayed systems and networks

Abstract

Summary This paper investigates the stabilization issue via event‐triggered controls (ETCs) for discrete‐time delayed systems (DDSs) and networks. Based on the recently proposed ETC scheme for discrete‐time systems without time delays, improved ETC (I‐ETC) and event‐triggered impulsive control (ETIC) are proposed for DDS. The algorithms for ETC, I‐ETC, and ETIC are given respectively to derive criteria of exponential stabilization of DDS. Moreover, the exponential stabilization and stabilization to ISS for discrete‐time delayed networks is achieved by employing the algorithms of ETC and ETIC. The issue of stabilization via ETCs for dynamical networks where different subsystems have different sequences of event instants is solved by introducing the check‐period into ETCs and establishing general ISS estimate of discrete‐time delayed inequality. In order to assess the performances of the control schemes, discussions on nontriviality are given by proposing the concept of rate of control and the function of control cost. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of theoretical results. From the obtained results on stabilization and the simulations, the ETIC is shown to have clear advantages and well performances than the classical state feedback control, the ETC recently proposed, I‐ETC, and the time‐based impulsive control on aspects of nontriviality, lower rate of control, lower cost of control, and robustness w.r.t. external disturbances.

Virtual Line Shafting-Based Total-Amount Coordinated Control of Multi-Motor Traction Power

“…A sliding mode controller is designed. Given its simplicity, high real-time performance and Substituting Equation (9) into Equation (11) yields Both the sliding mode arrival condition and Lyapunov stability theory indicate that the error can asymptotically converge to zero [28,29]. e 푠/(훿 + |푠|) function is typically used instead of the switching function sgn(푠), which can effectively suppress the chattering aroused by the sliding mode variable structure switching action to the control system [23,30].…”

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

“…We note that time delay exists in nonlinear control systems frequently . Moreover, the performance of the closed‐loop system may be degraded if time delay is not taken into consideration, and even destabilization of the control system maybe occur.…”

“…10,30 We note that time delay exists in nonlinear control systems frequently. [31][32][33] Moreover, the performance of the closed-loop system may be degraded if time delay is not taken into consideration, and even destabilization of the control system maybe occur. Therefore, impulsive delay systems are popular with many authors in the last years because of their plenty of real applications.…”

Periodic event‐triggered control with multisource disturbances and quantized states

“…Some interesting results have been obtained for different kinds of complex system, such as nonlinear systems, 1,2 multi-agent systems, 3,4 fuzzy systems, 5,6 stochastic systems, 7,8 and so on. Meanwhile, various types of ETC strategies have been proposed, such as self-triggered control, 9,10 continuous-time event-triggered control, 11,12 discrete-time event-triggered control 13,14 and adaptive event-triggered control, 15,16 etc. More recently, periodic event-triggered (PET) control has attracted considerable attention.…”