Upper Bound Of Sampling Period Research Articles

Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays

This paper studies the mean square exponential synchronization control of the Markovian jump chaotic Lur'e systems (MJCLSs) with multiple time delays under aperiodic sampling. Firstly, by introducing the mode-dependent single/double integral terms and considering the system state at the sampling instant, a new mode-dependent Lyapunov functional based on the looped-functional is constructed. On the basis of the constructed functional and by estimating the expectation of the solution of MJCLSs with multiple time delays, an exponential synchronization criterion in the mean square sense is presented. Then, based on the obtained stability conditions, a design method for aperiodic sampled-data controller (ASDC) to ensure the exponential synchronization is proposed. Finally, the effectiveness of the developed method is demonstrated by the Chua's circuit model and a neural network model. Compared with the existing literature, an admissible larger upper bound of sampling period can be obtained.

Leader-Following Consensus of Multiagent Systems via Asynchronous Sampled-Data Control: A Hybrid System Approach

In this article, we develop a hybrid system approach for sampled-data-based leader-following consensus of multiagent systems over a static/switching directed network. First, an asynchronous sampled-data hybrid consensus control protocol is proposed, which has an extra reset control part in contrast with the traditional linear control protocol and is beneficial for achieving better transient consensus performance. Then, with several properly defined internal variables, a hybrid model consisting of both flow and jump dynamics is constructed to describe the closed-loop dynamics. Based on this model and internal decreasing functions, Lyapunov-based stability conditions are derived, and larger upper bound of sampling period can be obtained compared to the existing related work. Finally, an example is given to show the superiority of the proposed approach.

Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation

In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficiently small sampling period. Considering the practical criterion for the size of sampling period, the upper bound of sampling period is estimated. Finally, an application example, an unstable Mackey–Glass model, is asymptotically stabilized by introducing a blood transfusion item with time-delayed sampled-data feedback control. The blood transfusion speed and blood collection test period are derived from the main results. Some simulations and comparisons show the correctness and advantages of the main theoretical results.

An Event-Triggered Consensus Control with Sampled-Data Mechanism for Multi-agent Systems

In this paper, an event-triggered control strategy with sampled-data mechanism is proposed to address the consensus problem for multi-agent system. The states of each agent are obtained periodically instead of continuous detection by using sampling technology. Rather than traditional Lyapunov technique, the system stability is analyzed by introducing a disagreement vector whose convergence is proved by contraction mapping, and a necessary condition about the upper bound of sampling period is derived under which systems could achieve consensus. Simulations results are presented to show the effectiveness of proposed event-triggered control strategy with sampled data mechanism compared to the basic one.

Further Results on Delay-Dependent Stability of Multi-Area Load Frequency Control

Further to results reported by Jiang <etal xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> , this paper investigates delay-dependent stability of load frequency control (LFC) emphasizing on multi-area and deregulated environment. Based on Lyapunov theory and the linear matrix inequality technique, a new stability criterion is proposed to improve calculation accuracy and to reduce computation time, which makes it be suitable for handling with multi-area LFC schemes. The interaction of delay margins between different control areas and the relationship between delay margins and control gains are investigated in details. Moreover, usage of delay margins as a new performance index to guide controller design is discussed, including tuning of the controller for a trade-off between delay tolerance and dynamic response, choosing the upper bound of the fault counter of communication channels and the upper bound of sampling period of a discrete realization of the controller. Case studies are carried out based on two-area traditional, two-area and three-area deregulated LFC schemes, all equipped with PID-type controllers, respectively. Simulation studies are given to verify the effectiveness of the proposed method.

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n − 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.

Sampling Period Selection for Digital Variable Structure Control

The selection of sampling period for digital variable structure control of linear systems is discussed in this paper. An algorithm is given to estimate the upper bound of sampling period that guarantees the pseudo-sliding along a prescribed sliding hyperplane. As demonstrated in the computer simulations, the algorithm gives a satisfactory approximation of the upper bound of sampling period