Global Robust Stability Research Articles

A global asymptotic synchronization problem via internal model approach

In this paper, we study the global robust synchronization problem of the controlled Duffing system and the van der Pol oscillator. By employing the internal model approach, we first convert the problem into a global robust stabilization problem of a time-varying nonlinear system in the lower triangular form. Then we show that the global robust stabilization problem of the lower triangular system is solvable, thus leading to the solution of the global robust synchronization problem.

Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay

The switching signal (switching law) design for robust global exponential stability of switched nonlinear systems is investigated in this paper. LMI-based delay-dependent criteria are proposed to design the switching signal and guarantee the global exponential stability. Free weighting matrix and additional nonnegative inequality approaches are used in this paper to find the less conservative stability results. Finally, some numerical examples are illustrated to show the main improvement.

On Global Robust Stability of a Class of Delayed Neural Networks with Discontinuous Activation Functions and Norm-Bounded Uncertainty

This paper considers the problem of global robust stability of a class of uncertain delayed neural networks with discontinuous activation functions. The uncertainties are assumed to be norm-bounded. In the form of linear matrix inequality (LMI), a new sufficient condition is obtained for the robust stability of this class of neural networks based on Lyapunov–Krasovskii stability theory as well as Filippov theory. Our conditions are independent of the delay and easy to check. A numerical example is given to show the effectiveness and superiority of our results.

Robust exponential stability for discrete‐time interval BAM neural networks with delays and Markovian jump parameters

AbstractThis paper investigates the problem of global robust exponential stability for discrete‐time interval BAM neural networks with mode‐dependent time delays and Markovian jump parameters, by utilizing the Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) approach. A new Markov process as discrete‐time, discrete‐state Markov process is considered. An exponential stability performance analysis result is first established for error systems without ignoring any terms in the derivative of Lyapunov functional by considering the relationship between the time‐varying delay and its upper bound. The delay factor depends on the mode of operation. Three numerical examples are given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.

Global robust stabilization of feedforward systems with uncertainties

This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.

Robust stability analysis of delayed Takagi-Sugeno fuzzy Hopfield neural networks with discontinuous activation functions

In this paper, the global robust stability problem of delayed Takagi-Sugeno fuzzy Hopfield neural networks with discontinuous activation functions (TSFHNNs) is considered. Based on Lyapunov stability theory and M-matrices theory, we derive a stability criterion to guarantee the global robust stability of TSFHNNs. Compared with the existing literature, we remove the assumptions on the neuron activations such as Lipschitz conditions, bounded, monotonic increasing property or the assumption that the right-limit value is bigger than the left one at the discontinuous point. Finally, two numerical examples are given to show the effectiveness of the proposed stability results.

Improved robust stability criteria for neural networks with fast time-varying delays

An improved robust global stability criterion is developed for uncertain neural networks with fast time-varying delays. The networks have norm-bounded parametric uncertainties. The relationship between the time-varying delay and associated extreme bounds (lower and upper) is appropriately exploited when dealing with the Lyapunov functional derivative. The developed stability criterion is delay dependent and is characterized by linear-matrix-inequality-based conditions. Numerical examples are presented to illustrate the benefits and lower conservativeness of the developed method.

Delay-dependent global robust stability criterion for neural networks with neutral-type time-varying delays

The problem of global robust stability for neural networks with neutral-type time-varying delays is investigated in this paper. Neutral differential equations are used to construct this class of neural networks. The time-varying delay function is bounded, and it is not required to be continuously differentiable. A new delay-dependent global stability criterion is derived based on the Lyapunov-Krasovskii functional approach. The criterion is formulated in terms of a linear matrix inequality. Numerical examples are given to illustrate the validity of the proposed stability criterion.

Global exponential robust stability of reaction–diffusion interval neural networks with continuously distributed delays

This paper considers the existence of the equilibrium point and its global exponential robust stability for reaction-diffusion interval neural networks with variable coefficients and distributed de...

A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.

New results for global robust asymptotic stability of BAM neural networks with time-varying delays

In this paper, the global robust asymptotic stability for a class of delayed bidirectional associative memory (BAM) neural networks with interval uncertainty is studied. Some less conservative conditions are presented for the BAM neural networks with multiple time-varing delays based on the Lyapunov functional approach. We also give one example to demonstrate the applicability and effectiveness of our results, and compare the results with the previous robust stability results derived in the literature.

Global robust asymptotic stability analysis of BAM neural networks with time delay and impulse: An LMI approach

The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays and impulse is studied. An approach combining the Lyapunov–Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

New results for robust stability of dynamical neural networks with discrete time delays

This paper deals with the global robust asymptotic stability of the equilibrium point of class of delayed neural networks having uncertain parameters whose values are unknown but bounded. By introducing a new upper bound norm for the interconnection matrix of the neural system and employing suitable Lyapunov functionals, we obtain new delay independent sufficient conditions for the uniqueness and global robust asymptotic stability of the equilibrium point. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. Some examples are constructed to compare the reported results with the related existing literature results.

A DELAY-DEPENDENT APPROACH TO ROBUST STABILITY FOR UNCERTAIN STOCHASTIC NEURAL NETWORKS WITH TIME-VARYING DELAY

This paper investigates the global delay-dependent robust stability in the mean square for uncertain stochastic neural networks with time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on a linear matrix inequality approach, globally delay-dependent robust stability criterion is derived by introducing some relaxation matrices which, when chosen properly, lead to a less conservative result. Two numerical examples are given to illustrate the effectiveness of the method.

Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.

GLOBAL ROBUST STABILITY OF TIME-DELAY SYSTEMS WITH DISCONTINUOUS ACTIVATION FUNCTIONS UNDER POLYTOPIC PARAMETER UNCERTAINTIES

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of dierential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.