Stabilization and Event-Triggered Control of Stochastic Delay Systems With Markovian Jump Parameters

Chunjie Xiao,Ting Hou

doi:10.1109/access.2020.3031389

Abstract

This article is concerned with the problem of delay-dependent stabilization for a class of stochastic Markov systems with event-triggered feedback control. An event-triggered mechanism (ETM) is proposed with the purpose of effectively reducing the transmissions of redundant massages, in which the generation of sensor sampling and control actuation is not periodic but only when some event-driven conditions are satisfied. In the meanwhile, a novel Lyapunov-Krasovskii functional (LKF) is applied to the closed-loop systems to establish the criterion of practically exponential mean-square stability. And a positive lower bound on the inter-execution times is guaranteed, that is, the Zeno behavior will not happen under this ETM. Furthermore, the event-triggered feedback controller can be constructed by solving the relevant linear matrix inequalities (LMIs). In the end, a numerical example displays the feasibility of our results.

Highlights

Stochastic time delay systems (STDSs) have been extensively investigated since they can exactly describe the dynamic processes that are influenced by the stochastic perturbations and time delays
Event-triggered control (ETC) mechanisms came into existence as strategies where the samplings and the updates of the control inputs are aperiodic and only with the occurrence of the certain events, in this manner, the utilization of communication resources was effectively improved while the required performance of systems can be satisfied
MAIN RESULTS This section establishes the practically exponential meansquare stability conditions for (5) by using the aforementioned event-triggered mechanism (ETM) while the existence of a positive lower bound on inter-execution times can be guaranteed, which means the Zeno behavior will not occur under our conditions

Summary

Introduction

Stochastic time delay systems (STDSs) have been extensively investigated since they can exactly describe the dynamic processes that are influenced by the stochastic perturbations and time delays. One can not deny that the above-mentioned time-triggered strategies may cause redundant transmissions and unnecessary waste of limited resources, especially for systems with presented communication constraints. Event-triggered control (ETC) mechanisms came into existence as strategies where the samplings and the updates of the control inputs are aperiodic and only with the occurrence of the certain events (see, e.g., [13]–[17]), in this manner, the utilization of communication resources was effectively improved while the required performance of systems can be satisfied. In [18], an eventtriggered real-time scheduling strategy was investigated for embedded systems to decide when the control task would be executed while the asymptotical stability was guaranteed. By using model transformation method, [19] remodeled ETC embedded systems as hybrid systems to establish the Lyapunov stability theorems for these

Objectives

Results

Conclusion