Delay-dependent Asymptotic Stability Criteria Research Articles

Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

<abstract><p>This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.</p></abstract>

A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.

Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays

The Lyapunov–Krasovskii functional approach is an important and effective delay-dependent stability analysis method for integer order system. However, it cannot be applied directly to fractional-order (FO) systems. To obtain delay-dependent stability and stabilization conditions of FO delayed systems remains a challenging task. This paper addresses the delay-dependent stability and the stabilization of a class of FO memristive neural networks with time-varying delay. By employing the FO Razumikhin theorem and linear matrix inequalities (LMI), a delay-dependent asymptotic stability condition in the form of LMI is established and used to design a stabilizing state-feedback controller. The results address both the effects of the delay and the FO. In addition, the upper bound of the absolute value of the memristive synaptic weights used in previous studies are released, leading to less conservative conditions. Three numerical simulations illustrate the theoretical results and show their effectiveness.

Delay-dependent asymptotic stability criteria for genetic regulatory networks with impulsive perturbations

This paper considers the problem for asymptotic stability of genetic regulatory networks with impulse control using the delay partitioning approach. By using the direct Lyapunov method, a new Lyapunov–Krasovskii functional is introduced based on the decomposition approach. Time delays here are assumed to be time-varying and belong to the given intervals. When dealing with the time derivative of Lyapunov functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by the Matlab LMI toolbox. Finally, the proposed method is validated through the numerical simulation, which shows the effectiveness of the presented stability criteria.

Stability analysis of decentralized event-triggered H∞ control using the quadratic convex approach

This paper studies the stability analysis of the decentralized event-triggered H∞ control with communication delays using the quadratic convex approach. Unlike the decentralized event-triggered mechanism (ETM), which only uses the information from the sensor itself by considering the communication topology of the wireless sensor network, a more general decentralized ETM is first proposed by using the information from both the sensor itself and its neighbours. Then, a time-delay system model with parameters of the decentralized ETM, directed graph information, communication delays and external disturbances is presented. In addition, novel delay-dependent asymptotic stability criteria are derived by using the augmented Lyapunov–Krasovski functional (LKF), which contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Unlike some prior results using the first-order convex combination property, our derivation applies the quadratic convex approach with the augmented LKF, which results in less conservatism. Moreover, sufficient conditions for the co-design of the controller and the decentralized ETM are obtained. Finally, numerical examples confirm the effectiveness of the proposed method.

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

This paper investigates the asymptotic stability problem for delayed genetic regulatory networks with reaction---diffusion terms under both Dirichlet boundary conditions and Neumann boundary conditions. First, by constructing a new Lyapunov---Krasovskii functional and using Jensen's inequality, Wirtinger's inequality, Green's second identity and the reciprocally convex approach, we establish delay-dependent asymptotic stability criteria that do not require a restriction of the upper bounds of the delays' derivatives being less than 1. Thus, the stability criteria that we establish are less conservative than the existing criteria and extend the range of applications of the theoretical results. In addition, it is shown that the obtained criterion under Dirichlet boundary conditions retains the information about the reaction---diffusion terms, while these do not exist in the criterion under Neumann boundary conditions. It is then theoretically presented that the stability criteria established in this paper are less conservative than the existing ones. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.

New Delay-Dependent Stability Criteria for Recurrent Neural Networks with Time-Varying Delays

This paper is concerned with the problem of delay-dependent asymptotic stability criterion for recurrent neural networks with time-varying delays. A new Lyapunov functional is introduced by considering the information of neuron activation functions adequately. By using the improved delay-partitioning method and reciprocally convex approach, a less conservative stability criterion is obtained in terms of linear matrix inequalities (LMIs). A numerical example is finally given to illustrate the effectiveness of the derived method.

LMI-based criterion for robust stability of 2-D discrete systems with interval time-varying delays employing quantisation / overflow nonlinearities

This paper is concerned with the problem of global asymptotic stability of a class of nonlinear uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space model with time-varying state delays. The class of systems under investigation involves norm bounded parameter uncertainties, interval-like time-varying delays and various combinations of quantisation and overflow nonlinearities. A linear matrix inequality-based delay-dependent criterion for the global asymptotic stability of such systems is proposed. An example is given to illustrate the effectiveness of the proposed method.

A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method.

Less Conservative Delay-dependent Asymptotic Stability Criteria for Stochastic Neural Networks of Neutral-type with Distributed Delay

Less Conservative Delay-dependent Asymptotic Stability Criteria for Stochastic Neural Networks of Neutral-type with Distributed Delay

Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays

The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

On delay-dependent robust stability of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays

Abstract This paper deals with the problem of a new delay-dependent robust stability criteria for a class of mixed neutral and Lur’e systems. The system has time-varying uncertainties, interval time-varying delays and sector-bounded nonlinearity. The proposed method is based on Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of linear matrix inequality (LMI). Numerical examples show the effectiveness of the proposed method.

Improved asymptotic stability criteria for neural networks with interval time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks (NNs) with time-varying interval delay is investigated. A new class of Lyapunov functional is constructed to derive some novel delay-dependent stability criteria. The obtained criterion is less conservative because free-weighting matrix method and the technique of dealing with some integral terms are considered. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Stability criteria for neutral uncertain systems with time-varying delays

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with time-varying delays. In order to establish a new delay-dependent criterion for asymptotic stability and robust stability of the systems, a Lyapunov-Krasovskii functional coupled with the Leibniz-Newton formula and an integral inequality approach are introduced to express the relationship between system states and their derivatives. The sufficient stability condition with delay dependence is obtained in terms of a linear matrix inequality (LMI). The LMI can be easily solved using convex optimization algorithms. Two examples are given to illustrate the advantages of the proposed method.

New asymptotic stability criteria for neural networks with time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.

Switched delay-dependent control policy for water-quality systems

A delay-dependent analysis and synthesis approach is established for a class of linear discrete-time switched systems with time-varying delays using switched Lyapunov–Krasovskii functionals (SLKFs). The problem of water-quality control is cast as the problem of delay-dependent ℒ2 gain analysis and synthesis. New delay-dependent asymptotic stability criteria are developed under arbitrary switching based on appropriately constructed SLKFs. Delay-dependent switched control feedback is then designed, based on state- and output-measurements, to render the corresponding switched closed-loop system delay-dependent asymptotically stable with a prescribed ℒ2 gain measure. The developed results are cast as linear matrix inequalities and tested by Matlab simulation on a representative water-quality example.

An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.

Novel delay-dependent asymptotical stability of neutral systems with nonlinear perturbations

This paper address the asymptotical stability of neutral systems with nonlinear perturbations. Some novel delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are less conservative than the previous ones, owing to the introduction of free-weighting matrices, based on a class of novel augment Lyapunov functionals. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.