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A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.

In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

In this paper, the problem of adaptive ℋ_∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, Lü and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an ℋ_∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.

This letter considers uncertain Lur'e systems of neutral type with sector and slope restrictions. By constructing a new Lyapunov functional, a novel delay-dependent criterion for absolute stability is derived in terms of linear matrix inequalities (LMIs). Two numerical examples are illustrated to show the effectiveness of the proposed method.

In this letter, the problem of feedback controller design to achieve synchronization for neural network of neutral type with stochastic perturbation is considered. Based on Lyapunov method and LMI (linear matrix inequality) framework, the goal of this letter is to derive an existence criterion of the controller for the synchronization between master and response networks.

In this paper, the problem of stability analysis of neural networks with discrete time-varying delays is considered. By constructing a new Lyapunov functional and some novel analysis techniques, new delay-dependent criteria for checking the asymptotic stability of the neural networks are established. The criteria are presented in terms of linear matrix inequalities, which can be easily solved and checked by various convex optimization algorithms. Three numerical examples are included to show the superiority of our results.

This paper proposes synchronization and chaotic communication for a class of Lur'e type discrete-time chaotic systems. The scalar outputs are suitably chosen in a flexible manner to be linear, nonlinear, or predictive, and along with the drive system are then written in an output injection form. Then with a suitable design of an observer-based response system, dead-beat performance is achieved for synchronization and chaotic communications. Then disturbances in the drive system are considered. Using an ℋ^∞ performance criterion, the disturbance is attenuated to a prescribed level by solving linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the dead-beat performance.

In this paper, a methodology to design a system that robustly synchronizes a master chaotic system from a sampled driving signal is developed. The method is based on the fuzzy Takagi–Sugeno representation of chaotic systems, from which a continuous-time fuzzy observer is designed as the solution of an LMI minimization problem such that the error dynamics have H_∞ disturbance attenuation performance. Then, from the dual-system approach, the fuzzy observer is digitally redesigned such that the performance is maintained for the sampled master system. The effectiveness of the proposed synchronization methodology is finally illustrated via numerical simulations of the chaotic Chen's system.

This paper presents a simple numerical scheme for estimating the attraction region of a fixed point in one-dimensional discrete-time chaotic systems controlled by the delayed-feedback method. This scheme employs the well-known linear matrix inequality approach. A systematic procedure for estimating the region is provided, and numerical examples are used to validate the results.

This paper investigates the nonexistence of a specific kind of periodic solutions in a class of nonlinear dynamical systems with cylindrical phase space. Those types of systems can be viewed as an interconnection of several simpler subsystems with the interconnecting structure specified by a permutation matrix. Frequency-domain conditions as well as linear matrix inequalities conditions for nonexistence of limit cycles of the second kind are established. The main results also define the frequency range on which cycles of the second kind of the system cannot exist. Based on this LMI approach, an estimate of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem. Numerical results demonstrate the applicability and validity of the proposed method and show the effect of nonlinear interconnections on dynamical behavior of entire interconnected systems.

In this paper, in order to show some interesting phenomena of fourth-order Chua's circuit with a piecewise-linear nonlinearity and with a smooth cubic nonlinearity and compare dynamics between them, different kinds of attractors and corresponding Lyapunov exponent spectra of systems are presented, respectively. The frequency-domain condition for absolute stability of a class of nonlinear systems is transformed into linear matrix inequality (LMI) by using the celebrated Kalman–Yakubovich–Popov (KYP) lemma. A stabilizing controller based on LMI is designed so that chaos oscillations of fourth-order Chua's circuit with the piecewise-linear nonlinearity disappear and chaotic or hyperchaotic trajectories of the system are led to the origin. Simulation results are provided to demonstrate the effectiveness of the method.

In this paper, a more general third-order chaotic system with attraction/repulsion function is introduced on the basis of [Duan et al., 2005]. A gallery of chaotic attractors, bifurcation diagrams and Lyapunov exponent spectra are presented to show the interesting phenomena of the given system. Based on the absolute stability theory and linear matrix inequality (LMI), a simple method of chaos control for the system is proposed and a stabilizing controller is derived such that chaos oscillations of the system disappear and all chaotic trajectories of it are led to certain equilibrium. Numerical simulations are provided to illustrate the efficiency of the proposed method.

In the industry process, the delayed time is possible to change, and the uncertainty of delayed time can sharply increase the difficulty of the control. Based on Time-Delay Dependent State Feedback Predictive Control (DDSFPC) algorithm and Lyapunov functional method, this thesis deals with the system with uncertain state time-delay. The delayed time is led into the matrix, a sufficient condition for the range of the uncertain delayed time is provided via LMI. It also provides the range of the delayed time, which can make sure of the stability of the system. The validity of the above condition is proved by representative example.