Dynamic event‐triggered control for linear time‐invariant systems with ‐gain performance

In this paper, a novel dynamic event‐triggered control scheme is presented for linear time‐invariant systems. Under this control scheme, criteria that guarantee the asymptotic stability and the ‐stability are derived, by which the triggered parameters and the feedback gain can be codesigned. The stability criteria are derived by using Lyapunov‐based analysis tools, and a new Lyapunov‐Krasovskii functional is constructed to further reduce conservatism. Moreover, the projection technique and the mathematical induction are introduced in the stability analysis. Compared with the existing results for static strategies, the proposed dynamic strategy is more flexible and generates fewer events. Finally, simulation examples are provided to demonstrate the effectiveness of this new scheme.     

Refined discretized Lyapunov functional method for systems with multiple delays

The previously proposed discretized Lyapunov functional method for systems with multiple delay is refined using variable elimination and Jensen inequality. The resulting new stability criterion is simpler. Numerical examples indicate that the new method is much less conservative for a given discretization mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

Adaptive event‐triggered control for nonlinear discrete‐time systems

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. Copyright © 2016 John Wiley & Sons, Ltd.     

Networked‐based stabilization via discontinuous Lyapunov functionals

This paper presents a new stability and L₂‐gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced by Naghshtabrizitextitet al. (Syst. Control Lett. 2008; 57 :378–385; Proceedings 26th American Control Conference, New York, U.S.A., July 2007) in the framework of impulsive system representation. Most of the existing works on the stability of NCS (in the framework of time delay approach) are reduced to some Lyapunov‐based analysis of systems with uncertain and bounded time‐varying delays. This analysis via time‐independent Lyapunov functionals does not take advantage of the sawtooth evolution of the delays induced by sample‐and‐hold. The latter drawback was removed by Fridman (Automatica 2010; 46 :421–427), where time‐dependent Lyapunov functionals for sampled‐data systems were introduced. This led to essentially less conservative results. The objective of the present paper is to extend the time‐dependent Lyapunov functional approach to NCS, where variable sampling intervals, data packet dropouts, and variable network‐induced delays are taken into account. The Lyapunov functionals in this paper depend on time and on the upper bound of the network‐induced delay, and these functionals do not grow along the input update times. The new analysis is applied to the state‐feedback and to a novel network‐based static output‐feedback H_∞ control problems. Numerical examples show that the novel discontinuous terms in Lyapunov functionals essentially improve the results. Copyright © 2011 John Wiley & Sons, Ltd.     

A Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems

This paper studies a Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems. The event‐triggered control closed‐loop system is formulated as a hybrid system model. Firstly, by viewing the event‐triggered control closed‐loop system as a feedback connection of two smaller hybrid subsystems, the Lyapunov‐based small‐gain theorems for hybrid systems are applied to design triggering conditions. Then, a new class of triggering condition, the safe, adjustable‐type triggering condition, is proposed to tune the parameters of triggering conditions by practical regulations. This is conducive to break the restriction of the conservation of theoretical results and improve the practicability of event‐triggered control strategy. Finally, a numerical example is given to illustrate the efficiency and the feasibility of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

Resilient control of networked control systems under deception attacks: A memory‐event‐triggered communication scheme

This paper considers resilient event‐triggered control problem for a class of networked systems subject to randomly occurring deception attacks. First, a new memory event‐triggered scheme (METS) is proposed to reduce the utilization of communication resources while maintaining desired system performance. Different from some existing event‐triggered schemes, some recently released packets are firstly utilized in the proposed METS, which provides a better flexibility to improve the system dynamics. Second, considering the security problem of the networked control systems, a randomly occurring deception attack model is employed where the bounded malicious signals are injected by the adversary. Considering both the effects of METS and deception attack, new type of networked control system model is constructed and the corresponding memory state‐feedback controller is designed. Then, sufficient conditions for the asymptotical stability of the systems are derived by using a Lyapunov functional technique. Finally, the obtained results are verified through a pendulum system, which demonstrates the effectiveness of the proposed methods.     

Robust stability of neutral systems: a Lyapunov‐Krasovskii constructive approach

In this paper, robust stability of uncertain linear neutral systems is analysed via a Lyapunov–Krasovskii constructive approach. This paper is the first attempt to compute the Lyapunov–Krasovskii functional for a given time derivative functional w(·) for the class of linear neutral type time delay systems. Copyright © 2004 John Wiley & Sons, Ltd.     

Exponential stability of output‐based event‐triggered control for switched singular systems

This paper presents the exponential stability of output‐based event‐triggered control for switched singular systems. An event‐triggered mechanism is introduced based on measure output, by employing the Lyapunov functional method and average dwell time approach, some sufficient conditions for exponential stability of the switched singular closed‐loop systems are derived. Furthermore, dynamic output feedback controller parameters are obtained. Lastly, a numerical example is given to illustrate the validity of the proposed solutions.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Finite ‐gain problem for networked control systems with delays via event‐triggered control

By using the integrals of the signals to construct the triggering condition, integral‐based event‐triggered control can relax the requirement of persistent decrease on the Lyapunov function and, then, may yield better sampling performance. This paper studies the disturbance rejection problem for the integral‐based event‐triggered control systems with transmission delays and observer‐based output feedbacks. An integral‐based triggering condition is employed to generate the events. Two asynchronous models are implemented in the different sides of the networks. The model in the observer node is used to detect the events, whereas the model in the controller node is used to calculate the control signals. This structure contributes to avoiding the Zeno behavior, and then, an estimation on the lower bound of the interevent times is provided. Moreover, the criteria on the parameter in the triggering condition and on the bounds of the transmission delays are given to guarantee the desired disturbance rejection performance. Finally, a numerical example is provided to illustrate the efficiency and feasibility of the obtained results.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability analysis of discrete‐time systems with time‐varying delays: generalized zero equalities approach

This paper suggests a generalized zero equality lemma for summations, which leads to making a new Lyapunov–Krasovskii functional with more state terms in the summands and thus applying various zero equalities for deriving stability criteria of discrete‐time systems with interval time‐varying delays. Also, using a discrete‐time counter part of Wirtinger‐based integral inequality, Jensen inequality, and a lower bound lemma for reciprocal convexity, the forward difference of the Lyapunov–Krasovskii functional is bounded by the combinations of various state terms including not only summation terms but also their interval‐normalized versions, which contributes to making the criteria less conservative. Numerical examples show the improved performance of the criteria in terms of maximum delay bounds. Copyright © 2016 John Wiley & Sons, Ltd.     

On exponential stability of linear networked control systems

This paper addresses exponential stability of linear networked control systems. More specifically, the paper considers a continuous‐time linear plant in feedback with a linear sampled‐data controller with an unknown time varying sampling rate, the possibility of data packet dropout, and an uncertain time varying delay. The main contribution of this paper is the derivation of new sufficient stability conditions for linear networked control systems taking into account all of these factors. The stability conditions are based on a modified Lyapunov–Krasovskii functional. The stability results are also applied to the case where limited information on the delay bounds is available. The case of linear sampled‐data systems is studied as a corollary of the networked control case. Furthermore, the paper also formulates the problem of finding a lower bound on the maximum network‐induced delay that preserves exponential stability as a convex optimization program in terms of linear matrix inequalities. This problem can be solved efficiently from both practical and theoretical points of view. Finally, as a comparison, we show that the stability conditions proposed in this paper compare favorably with the ones available in the open literature for different benchmark problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays

This paper discusses the problem of output feedback stabilization for a more general class of stochastic high‐order nonlinear systems with time‐varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed‐loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

Singularly perturbed implicit control law for linear time‐varying delay MIMO systems

This paper proposes a control scheme for the problem of stabilizing partly unknown multiple‐input multiple‐output linear time‐varying retarded systems. The control scheme is composed by a singularly perturbed controller and a reference model. We assume the knowledge of a number of structural characteristics of the system as the boundedness and the knowledge of the bounds for the unknown parameters (and their derivatives) that define the system matrices, as well as the structure of these matrices. The results presented here are a generalization of previous results on linear time‐varying Single‐Input Single‐Output (SISO) and multiple‐input multiple‐output systems without delays and linear time‐varying retarded SISO systems. The closed‐loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. The uniform asymptotic stability of the singularly perturbed retarded system is guaranteed. We show how to design a control law such that the system dynamics for each output is given by a Hurwitz polynomial with constant coefficients. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of a class of switched positive linear time‐delay systems

This paper addresses the problem of stability for a class of switched positive linear time‐delay systems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co‐positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co‐positive type Lyapunov–Krasovskii functional to the common co‐positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis and design of event‐triggered control algorithms using hybrid systems tools

This article proposes a general framework for analyzing continuous‐time systems controlled by event‐triggered algorithms. Closed‐loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event‐triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions. Using recently developed tools for robust stability, properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated by several event‐triggered strategies available in the literature, and observations about their key dynamical properties are made.     

Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

Robust control of T‐S fuzzy systems with time‐varying delay using new approach

This paper aims to design a controller to robustly stabilize uncertain nonlinear systems with time‐varying delay and norm bounded uncertainties via Takagi–Sugeno (T‐S) fuzzy model. The stabilization conditions are given in the form of linear matrix inequalities using a single Lyapunov–Krasovskii functional (LKF) combining the introduction of some relaxation matrices and only one tuning parameter. In comparison with the existing techniques in the literature, the proposed approach has two major advantages. The first is the reduction of computational complexity when the number of IF‐THEN rules, r, is big. The second concerns the conservatism reduction. Several examples are given to show the effectiveness and the merits of the design procedure. Copyright © 2009 John Wiley & Sons, Ltd.