Upper Bound Of Sampling Intervals Research Articles

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Improved stability and stabilization criteria of sampled-data control systems based on an enhanced looped-functional

This paper proposes improved stability and stabilization criteria that can increase the upper bound of sampling interval for the sampled-data systems while decreasing the computational complexity. To realize such improvement, an enhanced looped-functional is devised so that it can include 1) two time integrals of the weighted state derivative and 2) a single-integral quadratic terms with an augmented vector stacked with the state and its derivative. In addition, to aid the efficient use of the looped-functional, two zero equalities are newly established in the main derivation, which plays a key role in reinforcing the relationship between the time integrals of the weighted state derivative and other considered states. Furthermore, an improved free-matrix-based integral inequality is provided to obtain a tight upper bound on the single-integral quadratic terms in the stability analysis and control synthesis process. Finally, the validity of proposed method is verified through three numerical examples.

Aperiodic sampled-data synchronization of Markovian jump neural networks with partially known switching transition rates

In this paper, the aperiodic sampled-data synchronization problem of Markovian jump neural networks with partially known switching transition rates is investigated. The problem of asynchronous switching between the system mode and the controller mode is analyzed due to switching of the transition rate matrix. As the size constraint between the dwell time and the sampling interval, a sampling interval is divided into a matched interval and a mismatched interval to establish the error system models, respectively. Then, a set of multiple Lyapunov looped-functionals which consist of mode-dependent single/double/triple integral terms are constructed to analyze the mean-square exponential stability of the error system. Furthermore, a design method for aperiodic sampled-data controller is proposed. Finally, the obtained results are verified by some numerical simulations, and compared with the existing method, it shows that a larger upper bound of sampling interval can be obtained.

Aperiodic sampled-data control for local stabilization of memristive neural networks subject to actuator saturation: Discrete-time Lyapunov approach

In this paper, the local stabilization of memristive neural networks (MNNs) with actuator saturation is investigated via aperiodic sampled-data control. Inspired by the characteristic of the control scheme, a novel sampling-interval-dependent Lyapunov functional (SIDLF) is constructed. The main contribution of the developed Lyapunov functional lies in that the requirement on its positive definiteness is replaced by a looped condition. Then, using some inequality techniques and the discrete-time Lyapunov approach, two sufficient criteria are derived to ensure the locally asymptotical stability of the trivial solutions of closed-loop systems. A unified work is developed that can deal with the presence of the saturation nonlinearity effects, aperiodic sampled-data control, as well as SIDLF. Additionally, two convex optimization schemes, aiming at enlarging the admissible initial region (AIR) and maximizing the upper bound of sampling interval, are respectively presented for designing the desired saturated sampled-data controller gains. A quantitative relationship between the maximum sampling interval and AIR is revealed. Finally, two numerical examples are given to illustrate the advantages and effectiveness of the derived theoretical conclusions.

Non-fragile sampled-data control of network systems subject to time-delay

ABSTRACTThis paper studies the consensus problem of non-linear network systems subject to time-delay through aperiodic sampled-data control, which is more desirable and flexible than periodic sampling control. By receiving the relative information of the neighboring nodes, each node can obtain control input signals at the discrete sampling instants. A new stability criterion is established for network systems via using a time-dependent Lyapunov functional and the free-weighting matrix method. The maximum upper bound of sampling interval can be achieved by solving Linear matrix inequality optimization problem. Under the basic work of a non-fragile sampled-data controller, network systems with time-delay are asymptotically stable. In the end, two numerical simulation examples can be provided to illustrate the validity of the application of the proposed algorithm.

Synchronization of Network Systems Subject to Nonlinear Dynamics and Actuators Saturation

This paper investigates the synchronization of network systems with time-varying delay, nonlinear dynamics and actuators saturation through the use of sampled-data controllers. Using tools from free-weighting matrix approach and Lyapunov stability theory, sufficient conditions for the synchronization of network systems are derived. It is theoretically shown that the synchronization of network systems can be achieved if the controller gain is selected suitably. Furthermore, the upper bound of sampling intervals for achieving synchronization is estimated via a simple algorithm. The effectiveness of the obtained results is verified through two numerical examples.

Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data

In this paper, the problem of synchronization via sampled-data control is considered for stochastic delayed neural networks with Levy noise and Markovian switching. The purpose of the problem addressed is to derive a sufficient condition and a sampled-data control law such that the dynamics of the error system is stable in mean square, and thus the synchronization can be achieved for the master system and the slave system. By generalized Ito’s formula and the construction of Lyapunov functional, an LMI-based sufficient condition is established to ensure the synchronization of the two systems. The control law is determined simultaneously, which depends on the switching mode, time delay, and the upper bound of sampling intervals. A numerical example is provided to verify the usefulness of the proposed criterion.

Estimation of sampling interval based on Churilova's circle criterion systems with time-varying delay

A class of nonlinear continuous systems with discrete control is considered. Applying the input delay approach the system is transformed to system with time-varying sawtooth delay. Then an approach to estimate maximum upper bound of sampling interval using circle criterion for time-varying systems proposed by Churilova (1995) is described. Effectiveness and advantages of the method are illustrated by some numerical examples.

Sampled-data Consensus of Multi-agent Systems with General Linear Dynamics Based on a Continuous-time Model

This paper discusses the sampled-data consensus problem of multi-agent systems with general linear dynamics and time-varying sampling intervals. To investigate the allowable upper bound of sampling intervals, we employ the property of discretization of sampled-data to identify the upper bound on the variable sampling intervals via a continuous-time model. Without considering the states in the sampling intervals, the decrease of Lyapunov function is guaranteed only at each sampling time. Consequently, it results in a more robust sampling interval which is obtained by verifying the feasibility of LMIs. Subsequently, provided a limited matrix variable, the control gain matrix K is solved by the LMI approach. Numerical simulations are provided to demonstrate the effectiveness of theoretical results.

Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information

In this paper, the consensus problem for second-order multi-agent systems using impulsive control with sampled hetero-information is investigated. Necessary and sufficient conditions for sampling interval to achieve consensus for the second-order multi-agent systems are obtained. Analysis for the upper bound of sampling interval, convergence performance, and communication cost of the proposed control protocols are also discussed. Some numerical examples are given to demonstrate the effectiveness of the proposed control protocols.

Second-order consensus for directed multi-agent systems with sampled data

This paper deals with the consensus problem of second-order multi-agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi-agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time-varying piecewise-continuous delay and proposing a novel time-dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.