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In this paper, a class of linear discrete-time systems with input saturation is studied in a data-driven framework. Firstly, the input-state data are collected to represent the open-loop and closed-loop systems. While the open-loop data-based representation is a result that is parallel to system identification, the closed-loop representation bypasses the system identification and can be used for direct data-driven control law synthesis. Then, by a novel Lyapunov technique, sufficient conditions for system stability are derived, such conditions are independent of system matrices. Moreover, the attraction domain is estimated using two classes of shape reference sets. Finally, two examples are used to test the correctness of the data-driven control laws. [ABSTRACT FROM AUTHOR]

The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations. • Impulsive consensus algorithms based on velocity regulation are proposed for vector second-order Lipschitz nonlinear MASs. • The relationship between impulsive dynamical consensus and impulsive static consensus is analyzed. • A convex framework is proposed to design impulsive consensus gain matrices with guaranteed convergence rate. [ABSTRACT FROM AUTHOR]

This article considers the problems of achieving exponential stability and finite hybrid L2 × l2‐gain with respect to continuous and discrete disturbances for linear neutral time‐delay systems with impulsive effects. In the framework of descriptor system representation, a piecewise timer‐dependent Lyapunov functional is introduced to analyze the double impacts of state‐delay and impulse‐dwell‐time on stability of the underlying system. This functional depends on the state over an impulse interval and the state over a delay interval. Its construction is based on a delay‐fractioning scheme which ensures all delay subintervals contains at most one impulse instant. The relations among the augmented state variables are explored by using the impulse‐timer functions and the Newton–Leibniz formula. It is proved that the positive definiteness property of the functional at nonimpulse instants is not necessary for ensuring stability. The hybrid L2 × l2‐gain analysis is carried out by jointly using the introduced functional and a discrete‐time Lyapunov function. The obtain criteria for exponential stability and hybrid L2 × l2‐gain are expressed in terms of linear matrix inequalities. Their effectiveness is verified through two numerical examples. [ABSTRACT FROM AUTHOR]

Summary: The problem of impulsive stabilization of linear neutral delay systems is investigated by using the impulse‐time‐dependent Lyapunov functions. The construction of impulse‐time‐dependent Lyapunov functions is based on the singular system representation of the impulsively controlled neutral delay system. In order to overcome the difficulty arising from time‐varying state delays, a Razumikhin‐type analysis method is developed and the key technique is to establish the relation between the slow and fast state variables by using a difference inequality. The derived stability criterion weakens the restriction condition on the impulse operators found in the previous result. For constant delay case, an improved stability criterion is derived by applying an impulse‐time‐dependent Lyapunov functional. Next, based on the newly established stability criteria, novel sufficient conditions on the existence of impulsive controllers with range dwell‐time constraint are presented. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study addresses the problem of H∞ control for linear singular time‐delay systems subject to impulsive perturbations. Specifically, the impulses are allowed to be destabilising, i.e. they may degrade the closed‐loop performance of the considered systems. With the aid of a descriptor‐type impulse‐time‐dependent Lyapunov functional, a sufficient condition for the solvability of the problem is derived in terms of linear matrix inequalities (LMIs). By solving a set of LMIs, a desired state‐feedback controller is found, which guarantees that the closed‐loop system is impulse‐free, internally exponentially stable, and achieves a prescribed L2 ‐gain. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The H ∞ synchronization problem for complex dynamical networks with coupling delays and external disturbance via distributed impulsive control is studied. Two types of time-varying coupling delays are considered: the delays without any restriction on the delay derivatives, and the delays whose derivatives are strictly less than 1. A time-varying Lyapunov function/functional approach is applied to L 2 -gain analysis of the synchronization error systems. H ∞ synchronization criteria are established to guarantee the synchronization to be robust with respect to disturbance in the sense that the L 2 -gain from the disturbance to the control output is satisfactorily small. For each type of coupling delays, an algorithm involving convex optimization is proposed to design distributed impulsive controllers achieving a suboptimal value of the sum of coupling strengths for a prescribed L 2 -gain. Two numerical examples illustrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

This study considers impulsive observer‐based control of uncertain linear systems. A novel time‐varying Lyapunov function is introduced to explore the hybrid characteristic of the impulsive observed‐based control systems. By applying the time‐varying Lyapunov function method combined with convex combination technique, sufficient conditions for the existence of the impulsive observer‐based controller is derived in terms of linear matrix inequalities (LMIs). The control and observer gains can be obtained from the feasible solutions of the newly‐obtained LMI‐based conditions. Two numerical examples are presented to show the efficiency of the proposed design method. [ABSTRACT FROM AUTHOR]

This article is concerned with the design of impulsive observers with variable update intervals for Lipschitz nonlinear systems with delays in state. Discontinuous Lyapunov function/funtional approaches are developed to analyse the stability of error dynamics. Delay-independent sufficient conditions for uniform exponential stability of the error dynamics over variable update intervals are derived in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the observer gain matrix can be solved numerically with an LMI-based optimisation algorithm. Numerical examples are provided to show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, the problem of impulsive synchronization of two identical Lur''e systems via partial states is studied. The problem arises in the situation when only partial states of the driven systems are available. By using the method of the variation of parameters for linear impulsive systems and some analysis technique, a sufficient condition for the existence of the impulsive control law for synchronization via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices. By using this result, we propose a new impulsive synchronization scheme for a class of Lur''e systems. The new impulsive synchronization scheme only exerts the impulsive input on partial states of the driven system and is characterized by a set of conditions related to the impulsive interval bound, the impulsive magnitude and a coupling condition between them. The proposed impulsive synchronization method is illustrated through Chua''s circuit. [Copyright &y& Elsevier]

This paper addresses the impulsive observers design problem of perturbed Lipschitz nonlinear systems subject to noisy delayed discrete measurements. The transmission delay, state perturbation, and measurement noise simultaneously hinder the convergence of impulsive observer. To deal with the difficulty, the observation error system with delayed impulses is represented as an augmented system with switching delay-free impulses. By taking into account the switching structure of the impulse dynamics, the impulse observation gain matrix is modelled as a function of the time interval between two consecutive sampling instant and update instant. Such a structure of the observation gain matrix is able to adapt to the variation of sampling period and transmission delay. To obtain a tractable design condition, the idea of piecewise linear interpolation is applied to represent the impulse observation gain matrix as a piecewise linear form, which is determined by finite static impulse gains. A piecewise Lyapunov function which matches the piecewise linear structure of the observation gain is constructed to analyze the exponential input-to-state stability (EISS) property of the observation error system. The EISS gain quantifies the robustness performance of the designed impulsive observer. Sufficient conditions for the existence of the proposed variable gain impulsive observers are presented. Two numerical examples are provided to illustrate the effectiveness of the developed impulsive observation strategy. • A methodology for designing impulsive observers with delayed measurements and disturbances is proposed. • Based on the augmented representation of the observation error system, a piecewise linear gain function is constructed. • The robustness performance of the proposed observers against external disturbance is characterized by the notion of EISS. [ABSTRACT FROM AUTHOR]

In this paper, the problem of impulsive synchronization of two coupled delayed reaction–diffusion neural networks under aperiodic discrete measurements is revisited. Different from the previous static impulsive gain based impulsive synchronization strategy, a novel impulsive synchronization strategy using sampling-interval-dependent impulsive gains is proposed. The time-varying impulsive synchronization gains are able to adapt to the variation of sampling intervals, and thus can improve the synchronization performance. The stability analysis of the resultant synchronization error system is performed by applying an impulse-time-dependent discretized Lyapunov functions based method. Sufficient conditions for the existence of desired impulsive synchronization controllers are derived in terms of a set of linear matrix inequalities (LMIs). These conditions allow to synthesize time-varying impulsive gains. A numerical example is presented to demonstrate the effectiveness of the developed methodology. [ABSTRACT FROM AUTHOR]

This paper presents a study on impulsive H ∞ synchronization analysis of reaction–diffusion neural networks with discrete and distributed delays. It is assumed that the output information of the drive system is only available at discrete instants, and the dynamics of the response system are subject to external disturbance. To achieve H ∞ synchronization, an impulsive synchronization strategy is proposed which is based on feedback from the sampled-data of the drive and response dynamics. Novel time-dependent Lyapunov function/functional methods are developed for L 2 -gain analysis of synchronization error systems, both for fast-varying delays and for slowly-varying delays. LMI-based optimization methods are suggested to design impulsive H ∞ synchronization controllers with minimized feedback gain. Numerical simulations are provided to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the impulsive stabilization problem for a class of linear singular systems with time-delays. The stabilization is achieved by only exerting impulsive action on the slow state variables. Two novel Lyapunov methods are presented to determine exponential stability of the impulsively controlled systems. For the case where the time-delay is unknown and may be time-varying, a Lyapunov–Razumikhin method is developed, in which the Razumikhin condition is constructed by exploiting the relation among the fast state variables, the slow state variables, and their initial values. For the case where the delay derivative is strictly less than 1, a descriptor type of impulse-time-dependent Lyapunov functional is introduced, which is discontinuous at impulse times but does not grow along the state trajectories by construction. By using a convex technique, the stability criteria are expressed in terms of linear matrix inequalities (LMIs). Then, the impulsive controllers can be designed in the framework of LMIs. The effectiveness and advantages of the proposed methods are confirmed through simulation results. [ABSTRACT FROM AUTHOR]