Event‐based global stabilization of linear systems via a saturated linear controller

Zhang, Liangyin; Chen, Michael Z. Q.

doi:10.1002/rnc.3352

Cited by 57 publications

(23 citation statements)

References 34 publications

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“…Two cases will be considered below. If " > 0, from (37 ), we obtain 0 6 ( 36). If " D 0, from (37), we have k d i C1 < 0, which contradicts that .k/ > 0 for all k 2 N. Therefore, the relation k s i C1 6 k d i C1 holds.…”

Section: Remarkmentioning

confidence: 96%

“…Remarkably, to analyze the stability and the L 2 -gain properties of the resulting PETC systems, three different modeling and analysis frameworks based on impulsive systems, piecewise linear systems, and perturbed linear systems are established. Using the impulsive formulation following [28], a systematic technique to select the sampling period and design the PETC scheme is provided in [29].Notice that most of the previously mentioned approaches are performed in the continuous-time frame, very few works discuss the ETC in the discrete-time systems (e.g., [30][31][32][33][34][35][36] ), especially in the discrete-time nonlinear systems (e.g., [37]). In this paper, our interest is in the discrete-time nonlinear systems, because the discrete-time systems have their own interest and have found applications in various fields (e.g., [38]).…”

mentioning

confidence: 99%

“…Notice that most of the previously mentioned approaches are performed in the continuous-time frame, very few works discuss the ETC in the discrete-time systems (e.g., [30][31][32][33][34][35][36] ), especially in the discrete-time nonlinear systems (e.g., [37]). In this paper, our interest is in the discrete-time nonlinear systems, because the discrete-time systems have their own interest and have found applications in various fields (e.g., [38]).…”

mentioning

confidence: 99%

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Adaptive event‐triggered control for nonlinear discrete‐time systems

Yue

Yin

et al. 2016

Intl J Robust & Nonlinear

108

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This paper focuses on the analysis and the design of event-triggering scheme for discrete-time systems. Both static event-triggering scheme (SETS) and adaptive event-triggering scheme (AETS) are presented for discrete-time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event-triggering condition. The sufficient conditions of asymptotic stability of the closed-loop event-triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event-triggering schemes are illustrated on a practical example. 4105Similar ETC scheme can be found in [7]. A self-triggered scheme is given in [8] for continuoustime linear systems with disturbance, while guaranteeing the finite-gain L2 stability of the resulting self-triggered feedback control systems. In [9], a distributed relative-difference ETC scheme for distributed networked control systems with data dropout and transmission delays is proposed for linear and nonlinear subsystems. A decentralized relative-difference event-triggering mechanism is proposed for continuous-time linear systems in [10], where the closed-loop stability and L 1 performance and the bounds on the minimum time between two subsequent events generated by each node are also studied. More recently, a relative-difference discrete event-triggered communication scheme has been proposed in [11,12], where the term discrete refers to the fact that the approach needs the triggering condition to be checked only at discrete times, which is completely different from the preceding works where the implementation of the designed ETC schemes requires a continuous supervision of the system state to detect whether it violates the triggering condition. Also, an H 1 performance analysis and control synthesis of networked continuous-time linear systems with transmission delays are established in terms of linear matrix inequalities, which successfully solves the open problem in the previous published papers. Up to now, there are several interesting extensions to the research presented in [11], including event-triggered quantized control design problem for networked linear systems [13-15], event-based H 1 filter design problem for networked systems [16][17][18], L 2 -gain analysis of event-triggered networked linear systems [19], a co-design method of the ETC scheme and state feedback controller for networked T-S fuzzy systems and linear systems in [20] and [21], respectively, event-based H 2 and H 1 control design for discrete-time networked linear systems in [22] , output feedback control design for networked control systems [12,23], a decentralized state-dependent tr...

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Section: Remarkmentioning

confidence: 96%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Adaptive event‐triggered control for nonlinear discrete‐time systems

Yue

Yin

et al. 2016

Intl J Robust & Nonlinear

108

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“…There are also recent results on event-triggered control of linear systems with actuator saturation. [25][26][27] However, positive systems subject to actuator saturation under an event-triggered control strategy have not been studied.…”

Section: And Shen and Lam 11 )mentioning

confidence: 99%

“…Many results in the literature (see, eg, other works) devote to the analysis and design problems for linear systems with saturation nonlinearities. There are also recent results on event‐triggered control of linear systems with actuator saturation . However, positive systems subject to actuator saturation under an event‐triggered control strategy have not been studied.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered constrained control of positive systems with input saturation

Yin

Lin

Liu

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.

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Dynamic Output Feedback Control for Systems Subject to Actuator Saturation via Event‐Triggered Scheme

Zuo

Wang

2017

Asian Journal of Control

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In this paper, the event-triggered dynamic output feedback control problem for linear systems with actuator saturation is investigated. Event-triggered scheme only transmits the corresponding signal when the event-triggered condition is violated. Due to its advantage of saving communication resources, it is utilized to design the dynamic output feedback controller. A criterion is established to guarantee the stability of the closed-loop system by introducing an exponential term for the Lyapunov function, which corresponds to the exponential term in the event-triggered condition. The explicit design of the coefficient matrices of the controller is presented. Furthermore, a lower bound of the inter-event time is calculated to avoid Zeno behavior. An optimization algorithm is then formulated to maximize the estimation of the domain of attraction. Finally, a numerical example is given to illustrate the effectiveness of our methods and to show the trade-off between the size of the domain of attraction and communication resources saving.

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Event‐based global stabilization of linear systems via a saturated linear controller

Cited by 57 publications

References 34 publications

Adaptive event‐triggered control for nonlinear discrete‐time systems

Adaptive event‐triggered control for nonlinear discrete‐time systems

Event‐triggered constrained control of positive systems with input saturation

Dynamic Output Feedback Control for Systems Subject to Actuator Saturation via Event‐Triggered Scheme

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