Wajaree Weera

Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays

In this paper, we consider exponential stability problem for neutral-type neural networks with both interval time-varying state and neutral-type delays under more generalized activation functions. We note that discrete and neutral delays are both time-varying where the discrete delay is not necessarily differentiable and the information on derivative of neutral delay is not required. To the best of our knowledge, this is the first study under this conditions on discrete and neutral delays. Furthermore, we consider the case when there are interconnections between past state derivatives, namely, neural networks contain activation function of past state derivatives. Based on the Lyapunov-Krasovskii functional, we derive new delay-dependent exponential stability criteria in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Finally, numerical examples are given to illustrate the effectiveness of theoretical results and to show less conservativeness than some existing results in the literature.

Guaranteed Cost Control for Exponential Synchronization of Cellular Neural Networks with Mixed Time-Varying Delays via Hybrid Feedback Control

The problem of guaranteed cost control for exponential synchronization of cellular neural networks with interval nondifferentiable and distributed time-varying delays via hybrid feedback control is considered. The interval time-varying delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov-Krasovskii functionals is combined with Leibniz-Newtons formula and the technique of dealing with some integral terms. New delay-dependent sufficient conditions for the exponential synchronization of the error systems with memoryless hybrid feedback control are first established in terms of LMIs without introducing any free-weighting matrices. The optimal guaranteed cost control with linear error hybrid feedback is turned into the solvable problem of a set of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.

Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays

The problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works.

Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings

This paper presents the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling. The function projective synchronization of this model via hybrid adaptive pinning controls and hybrid adaptive controls, composed of nonlinear and adaptive linear feedback control, is further investigated in this study. Based on Lyapunov stability theory combined with the method of the adaptive control and pinning control, some novel and simple sufficient conditions are derived for the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling, and the derived results are less conservative. Particularly, the control method focuses on how to determine a set of pinned nodes with fixed coupling matrices and strength values and randomly select pinning nodes. Based on adaptive control technique, the parameter update law, and the technique of dealing with some integral terms, the control may be used to manipulate the scaling functions such that the drive system and response systems could be synchronized up to the desired scaling function. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Exponential stabilization of neutral-type neural networks with interval non-differentiable and distributed time-varying delays

In this paper, the problem of exponential stabilization of neutral-type neural networks with various activation functions and interval non-differentiable and distributed time-varying delays is considered. The interval time-varying delay function is not necessary to be differentiable. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newtons formula, the proposed stability criteria are formulated in the form of a linear matrix inequalities. Numerical example illustrates the effectiveness of the results.