Zhi-Hong Guan

Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach

In this paper, the problem of exponential stability in mean square for stochastic systems with multiple delays is investigated. A delay-dependent sufficient condition is derived in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Moons inequality for bounding cross terms. The criteria obtained in this paper can be tested numerically very efficiently using interior point algorithms. An example shows that the proposed methods are less conservative than the other methods.

Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control

In this paper, the synchronization of complex dynamical networks (CDNs) with system delay and multiple coupling delays is studied via impulsive distributed control. The concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes. The control topology can be designed either to be the same as the non-delayed coupling topology of the network, or to be independent of the intrinsic network topology. Based on the concept of control topology, an impulsive controller is designed to achieve the exponential synchronization of CDNs, and moreover, the exponential convergence rate can be specified. Illustrated examples have been given to show the effectiveness of the proposed impulsive distributed control strategy.

On delayed impulsive Hopfield neural networks

Many evolutionary processes, particularly some biological systems, exhibit impulsive dynamical behaviors, which can be well described by impulsive Hopfield neural networks. This paper formulates and studies a model of delayed impulsive Hopfield neural networks. Several fundamental issues such as global exponential stability, existence and uniqueness of the equilibrium of such networks are established. A numerical example is given for illustration and interpretation of the theoretical results.

Feedback and adaptive control for the synchronization of Chen system via a single variable

This Letter addresses control for the synchronization of chaotic Chen systems via a single variable. Two control approaches, namely a linear feedback controller and an adaptive controller, are investigated. In both cases sufficient conditions for the synchronization are obtained analytically. The control performances are verified by numerical simulations.

An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay

This paper considers the problem of exponential stability analysis of neural networks with time-varying delays. The activation functions are assumed to be globally Lipschitz continuous. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally exponentially stable. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the reduced conservativeness of the proposed results.

Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays

This note concerns the robust guaranteed cost control problem for a class of continuous-time Markovian jump linear system with norm-bounded uncertainties and mode-dependent time-delays. The problem is to design a memoryless state feedback control law such that the closed-loop system is stochastically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on linear matrix inequality, delay-dependent sufficient conditions for the existence of such controller are derived by using a descriptor model transformation of the system and by applying Moons inequality for bounding cross terms. Sufficient conditions which depend on the difference between the largest and the smallest time-delays are also presented. Two numerical examples are given for illustration of the proposed theoretical results.

On impulsive autoassociative neural networks

Many systems existing in physics, chemistry, biology, engineering, and information science can be characterized by impulsive dynamics caused by abrupt jumps at certain instants during the process. These complex dynamical behaviors can be modeled by impulsive differential systems or impulsive neural networks. This paper formulates and studies a new model of impulsive autoassociative neural networks. Several fundamental issues, such as global exponential stability and existence and uniqueness of equilibria of such neural networks, are established.

Impulsive consensus algorithms for second-order multi-agent networks with sampled information

In this paper, the distributed consensus problem for second-order continuous-time multi-agent networks with sampled-data communication is investigated. Motivated by impulsive control strategy, two kinds of impulsive distributed consensus algorithm are proposed. These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks. It is shown that the control gains, the sampling period and the eigenvalues of the Laplacian matrix of the communication graph play key roles in achieving the consensus. A numerical example is given to illustrate the results.

Sliding-Mode Velocity Control of Mobile-Wheeled Inverted-Pendulum Systems

There has been increasing interest in a type of underactuated mechanical systems, mobile-wheeled inverted-pendulum (MWIP) models, which are widely used in the field of autonomous robotics and intelligent vehicles. Robust-velocity-tracking problem of the MWIP systems is investigated in this study. In the velocity-control problem, model uncertainties accompany uncertain equilibriums, which make the controller design become more difficult. Two sliding-mode-control (SMC) methods are proposed for the systems, both of which are capable of handling both parameter uncertainties and external disturbances. The asymptotical stabilities of the corresponding closed-loop systems are achieved through the selection of sliding-surface parameters, which are based on some rules. There is still a steady tracking error when the first SMC controller is used. By assuming a novel sliding surface, the second SMC controller is designed to solve this problem. The effectiveness of the proposed methods is finally confirmed by the numerical simulations.

Consensus of Multi-Agent Networks With Aperiodic Sampled Communication Via Impulsive Algorithms Using Position-Only Measurements

In this technical note, an impulsive consensus algorithm is proposed for second-order continuous-time multi-agent networks with switching topology. The communication among agents occurs at sampling instants based on position only measurements. By using the property of stochastic matrices and algebraic graph theory, some sufficient conditions are obtained to ensure the consensus of the controlled multi-agent network if the communication graph has a spanning tree jointly. A numerical example is given to illustrate the effectiveness of the proposed algorithm.