Networked‐based H_∞ control for discrete‐time slow sampling singularly perturbed systems via an improved event‐triggered approach

Abstract

This paper investigates the H∞ control problem for a class of slow sampling singularly perturbed systems (S3PSs) with an improved event‐triggered method (ETM). Compared with the conventional static ETM, an improved one with time‐varying threshold is exploited to enhance the dynamic performance for the S3PSs with certain communication frequency reduction. By adjusting the threshold with the triggering error, a faster converge speed can be achieved. Sufficient conditions are derived by constructing a singular perturbation parameter (SPP) dependent Lyapunov function, with which both asymptotic stability can be guaranteed for the closed‐loop S3PSs and the ill‐conditioned numerical issues can be avoided. By resorting to the matrix inequality techniques, an ETM‐based controller can be developed within the upper bound of the SPP. Further demonstration for the feasibility of the proposed algorithm is presented by designing an ETM‐based controller for an inverted pendulum system.

Time‐regularization event‐triggeredH∞control for switched linear systems with frequent asynchronism

“…Compared with time-triggered mechanism, event-triggered mechanism (ETM) will only perform sampling when the pre-designed triggering requirements are met. Therefore, scholars have extensively and comprehensively explored the theory associated with ETC [20][21][22][23][24]. For example, a dynamic event-triggered optimal control scheme was generated for nonlinear Markov jump systems by introducing internal dynamic variables [25].…”

Input‐based event‐triggered control of a discrete‐time singularly perturbed system under a resource constrained environment

“…Some time-triggered sampling results related to network-controlled SPSs can be found in the literature (see [28] and references therein). However, there are limited results on an ETM for NCSs by considering the two-time-scale properties of a singularly perturbed system [29,30]. When these SPSs are controlled through a constrained network for many practical applications, continuous or periodic feedback leads to over-utilization of resources.…”

“…In [22], the authors surveyed discrete two-time-scale systems and documented their important applications. Therefore, the study of ETM for discrete-time network-controlled SPS is significant from practical and theoretical perspectives (see [34,35] and references therein.) In [36], a stabilized ETM is proposed for SPSs by using only slow dynamics.…”

“…However, the designed triggered mechanism in [36] does not ensure the nonexistence of Zeno phenomena. In [29,37], ETMs are proposed for the slow-sampling model of SPSs where both slow and fast dynamics are sampled at a slower rate. In case of slow-sampling model, ETMs will enforce the fast dynamics to sample at a slower rate which can cause undersampling.…”

H∞ containment of networked MASs with disturbances, position, and velocity constraints

“…And for all we know, no containment control result considers state constraints and disturbance simultaneously. $$$ {H}_{\infty } $$$ control is a classical robust control method, which has been used widely to deal with disturbances [31, 32]. Some $$$ {H}_{\infty } $$$‐based control strategies were applied to solve the consensus problem [33], containment problem [34], and formation problems of the MASs [35].…”