On Static and Dynamic Triggered Mechanisms for Event-Triggered Control of Uncertain Systems
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On Static and Dynamic Triggered Mechanisms for Event-Triggered Control of Uncertain Systems Dinh Cong Huong1
· Van Thanh Huynh2
· Hieu Trinh2
Received: 9 December 2019 / Revised: 16 March 2020 / Accepted: 18 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This study presents both static and dynamic event-triggered mechanisms for the design of event-triggered stabilizing state feedback controllers for a class of uncertain nonlinear systems. Sufficient conditions based on linear matrix inequalities are first provided to guarantee the asymptotic stability of the closed-loop system. The controllers are then systematically designed. We also prove that the inter-event intervals of the considered event-triggered mechanisms are positive, therefore ensuring that the Zeno behavior does not happen. Two examples with simulations are provided to illustrate the theoretical results. Keywords Event-triggered control · Lipschitz nonlinear function · Lyapunov direct method · Static event-triggered mechanism · Dynamic event-triggered mechanism · Linear matrix inequalities (LMIs)
1 Introduction The problems of stability analysis and control for dynamical systems have been widely considered in the literature since they have many practical applications (see, for example [1,3,7,8] and the references therein). Closed-loop feedback control systems, such as power systems, manufacturing systems and chemical processes, are normally implemented on a digital platform. Since the controller communicates with the plant via a shared digital channel, the information of the plant is first sampled
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Dinh Cong Huong [email protected] Van Thanh Huynh [email protected] Hieu Trinh [email protected]
1
Department of Mathematics and Statistics, Quy Nhon University, Binh Dinh, Vietnam
2
School of Engineering, Deakin University, Geelong, VIC 3217, Australia
Circuits, Systems, and Signal Processing
and then transmitted to the controller. One traditional digital control technique is the periodically triggered sampling, which allows us to design and analyze the performance of the controllers by using the well-known sampled-data system theory [1,3]. However, the periodically triggered sampling approach often requires more energy, computation and communication resources, while those resources may be used for other tasks (see, [2,13,20,23,24]). As such, event-triggered control is an intriguing approach borne out of the classical periodically triggered control approach (see, for example [4,6,9,14–16,18,21,22,25]). Under an event-triggered control law, samples of data are not updated periodically but only when some events have occurred. Therefore, it is deemed more efficient in terms of utilization of limited bandwidth and energy resources. So far, event-triggered control has been applied to solve important problems such as the event-triggered stabilization problem [16], the event-triggered tracking problem [17,19] and the event-triggered output regulation problem [10,11]. Most of the above works
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