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The units of networks, composed of systems, may converge to the same behavior in a fixed settling time, known as fixed‐time synchronization. In this paper, the problem of fixed‐time outer synchronization of double‐layered multiplex networks is studied. To synchronize the networks, delayed feedback controllers are designed. To guarantee the fixed‐time synchronization, some sufficient criteria are derived. The controllers and sufficient criteria can be applied to undirected and directed networks. The fixed settling time is related to controllers, the number of nodes for networks, and the dimension of node. Some numerical examples are provided to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this article, we study the reachable set estimation and controller design problems for a class of discrete time‐varying‐delay singularly perturbed systems. First, by constructing a ε‐dependent Lyapunov–Krasovskii functional and using reciprocally convex inequality, delay‐dependent conditions are obtained to ensure the state of the system under zero initial conditions is contained by an ellipsoid for any singularly perturbed parameters below a given threshold. Second, by the method of designing a state‐feedback controller, sufficient conditions that the reachable set of the closed‐loop system can be included in a given ellipsoid are obtained for admissible singularly perturbed parameters. Finally, two examples are given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper revisits the problem of H∞ filter design for singular systems with interval time‐varying delays. Firstly, by state decomposition method (SDM), a novel Lyapunov–Krasovskii functional (LKF) including two augmented nonintegral terms is presented. Secondly, via the constructed LKF and the linear matrix inequality (LMI) technique, sufficient stability conditions with lower conservatism are achieved such that the considered singular system is admissible with specified H∞ performance level. Thirdly, a state decomposition‐recombination approach is first introduced to obtain a desired H∞ filter in terms of matrix component transformation technology. Finally, the validity and superiority of the results obtained are verified via two numerical examples. [ABSTRACT FROM AUTHOR]

Sampled‐data based quantisation control for Takagi–Sugeno (T–S) fuzzy switched systems with actuator failures under asynchronous switching is studied. By the T–S fuzzy model, sampled‐data based asynchronous control is extended into switched non‐linear systems. An improved functional method is introduced. Applying this method, improved Lyapunov functionals are constructed. These functionals are mode dependent and piecewise continuous; not every term of these functionals is required to be positive definite; sampling states at both sides of sampling intervals are introduced into these functionals. More useful information with respect to system states is reflected in constructing functionals. Combining these functionals with the averaged dwell time technique, stabilisation conditions are relaxed, and improved exponential stabilisation criteria are obtained with less conservatism. In addition, variation ranges of membership functions are taken into account to reduce conservatism. Then, a sampled‐data based fuzzy quantisation controller is designed. Simulation examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study addresses the consensus problem of multi‐agent systems by combining adaptive control protocol and event‐triggered communication strategy. Two adaptive protocols are designed to guarantee the consensus. The event‐triggered communication strategy is utilised to save communication and reduce channel occupation. Each agent in the system sends its state to neighbours only at some irregular event instants determined by an appropriately designed event‐triggering condition. At first, the distributed event‐triggering condition of an agent only employs the state of its own and the state of the neighbours at their latest event instants. Later, another event‐triggering condition is given such that no global parameter is required for agents, such as the maximum eigenvalue of the Laplacian matrix. It is proven that the system can reach consensus by utilising the proposed control method. Illustrative examples are given to show the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

The problem of H∞ deconvolution filter design for a class of singular Markovian jump systems with time-varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov-Krasovskii functional, novel delay-dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. [ABSTRACT FROM AUTHOR]

It has been very popular to design a controller to attain multiple objectives in many engineering applications in the past few years. The so-called mixed H2/H∞ control is a typical this kind of case. Generally speaking, the problem of mixed H2/H∞ control is to find a controller not only to minimize the H2 performance (cost function) but also to satisfy the H∞ performance in spite of the worst disturbance, see references [1-6]. To mention one of them, Yang et al. [2] has studied the robust mixed H2/H∞ control problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities, which are represented by stochastic variables, have been tackled with by a new approach; the uncertainties, which are described as deterministic norm-bounded parameter perturbations, have been dealt with by the celebrated S-procedure. The resulting closed-loop system is exponentially mean square quadratically stable and attains the H2 control performance with a prescribed H1 attenuation level. Hence, from the practical engineering application point of view, the mixed H2/H∞ controller design problem has an obvious physical meaning. In some industrial applications, such as automobiles, manufacturing plants, and aircrafts, system components (the physical plant, the sensor, and the controller) are located at different places, [ABSTRACT FROM AUTHOR]

In this study, the problem of fault detection for a class of discrete‐time non‐linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full‐order mode‐dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality‐based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method. [ABSTRACT FROM AUTHOR]

This study studies the problem of distributed containment control for multi‐agent systems with higher‐order dynamics under directed network topologies. The higher‐order model‐based containment controllers with relative damping and absolute damping are proposed, respectively. It is shown that under the proposed containment controllers the followers will converge to the convex hull spanned by the leaders if for each follower, there exists at least one leader that has a directed path to the followers; the final states of the followers depend on the network topology as well as the initial states of the references models of the leaders. The second‐order model‐based containment controllers are discussed as special cases. Simulation examples are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of stochastic stability analysis for a class of genetic regulatory networks with Markovian jump parameters and time-varying delays. A delay-dependent stability criterion is derived by using a novel mode-dependent Lyapunov functional. The derived stability criterion is expressed in terms of linear matrix inequalities and is less conservative than the existing ones in the literature. A numerical example is provided to demonstrate the effectiveness of the proposed stability criterion. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]