Delay-dependent Stability Criteria Research Articles

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.

Stability analysis for linear time-delay systems using new inequality based on the second-order derivative

This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.

Fault-tolerant output-feedback stabilization for complex-valued neural networks with time delay and actuator failures

The paper considers the issue of fault-tolerant output-feedback stabilization for complex-valued neural networks with both time delay and actuator failures. The aim is to design a fault-tolerant output-feedback controller to ensure the network to be asymptotically stable. By using the discretized Lyapunov-Krasovskii functional method as well as the free-weighting matrix approach, a delay-dependent stability criterion is proposed. Then, with the aid of some decoupling techniques, a method for the design of desired output-feedback fault-tolerant controller is developed. Finally, a numerical example is given to verify the effectiveness of the present stabilizing method.

Delay-Dependent Stability Analysis of Network-Based Load Frequency Control of One and Two Area Power System with Time-Varying Delays

Network-based load frequency control (LFC) requires data transmission from the plant site to the control center and control center to the plant site. Communication delays resulting from an open communication network impart time-varying nature to network delay. This time-varying delay may debase the dynamic performance or instability of the LFC systems. Stability of the LFC system is investigated by Lyapunov–Krasovskii functional (LKF) analysis and linear matrix inequalities (LMIs) techniques. In this paper, a less conservative delay-dependent stability criterion is derived for the time-delay system by proper constructing of LKF and imposing tighter bounding of integral terms on time-derivative of LKF. Delay margin is obtained by solving proposed stability criterion for a time-delay LFC system equipped with a proportional-integral controller. The adequacy of the proposed result is confirmed using simulation studies.

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 and Order-Dependent Stability and Stabilization of Fractional-Order Linear Systems With Time-Varying Delay

Stability of fractional-order (FO) delayed systems remains a formidable problem. In this brief, asymptotic stability and stabilization of FO linear systems with time-varying structured uncertainties and time-varying delay are discussed. By employing FO Razumikhin theorem, two new delay-dependent and order-dependent stability criteria in form of LMI for FO nominal systems and FO uncertain sytems are first formulated, respectively. Moreover, state feedback controllers of stabilization are also derived with the help of the proposed stability criteria. The numerical simulation demonstrates the effectiveness of the theoretical formulation.

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.

Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays

In this paper, the robust stability problem for a class of uncertain stochastic complex-valued neural networks (USCVNNs) with additive time-varying delays (ATDs) is discussed. By constructing a suitable Lyapunov–Krasovskii functional (LKF), more time delay information is considered. By employing integral inequalities, some delay-dependent stability criteria are derived by converting USCVNNs into an equivalent real-valued uncertain stochastic neural networks. The obtained stability criterion is presented in the form of linear matrix inequalities (LMIs), which can be calculated through MATLAB LMI toolbox. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

Decentralised event-triggered impulsive synchronisation for semi-Markovian jump delayed neural networks with leakage delay and randomly occurring uncertainties

ABSTRACTThis study examines the problem of decentralised event-triggered impulsive synchronisation for the semi-Markovian jump neutral type neural networks with leakage delay and randomly occurring uncertainties. An improved globally asymptotic stability criterion is derived to guarantee impulsive synchronisation of the response systems with the drive systems. In order to reduce the network traffic and the resource of computation, we propose a new decentralised event-triggered scheme for the considered delayed NNs. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed. By establishing a suitable Lyapunov–Krasovskii functional (LKF) with triple integral terms and applying Writinger based integral method, auxiliary function based integral inequalities, reciprocal convex approach and improved inequality techniques, a delay dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

Improved Delay-dependent Stability Criteria for Networked Control System with Two Additive Input Delays

This paper is concerned with stability criteria of networked control system with two additive time-varying delay components. Firstly, by separating the whole delay interval into subintervals and using a new inequality in combination with convex polyhedron method, a less conservative criterion is proposed and an approach of stabilization controller design is given based on the obtained criterion. Secondly, a congruent condition and an extended condition with the same allowable delay upper bound are respectively deduced by using two different inequalities. Finally, some numerical examples are presented to illustrate the effectiveness of the obtained method.

Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.

Delay-Dependent Stability Analysis in Haptic Rendering

Nowadays haptic devices have lots of applications in virtual reality systems. While using a haptic device, one of the main requirements is the stable behavior of the system. An unstable behavior of a haptic device may damage itself and even may hurt its operator. Stability of haptic devices in the presence of inevitable time delay in addition to a suitable zero-order hold is studied in the presented paper, using two different methods. Both presented methods are based on Lyapunov-Krazuvskii functional. In the first method, a model transform is performed to determine the stability boundary, while the second approach is based on Free Weighing Matrices (FWMs). Delay-dependent stability criteria are determined by solving Linear Matrix Inequalities (LMIs). Results of these two methods are compared with each other and verified by simulations as well as experiments on a KUKA Light Weight Robot 4 (LWR4). It is concluded that using free weighing matrices leads to more unknown parameters and needs more calculation, but its results are less conservative.

Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays

This paper studies the global asymptotic stability problem for a class of stochastic complex-valued neural networks (SCVNNs) with probabilistic time-varying delays as well as stochastic disturbances. Based on the Lyapunov–Krasovskii functional (LKF) method and mathematical analytic techniques, delay-dependent stability criteria are derived by separating complex-valued neural networks (CVNNs) into real and imaginary parts. Furthermore, the obtained sufficient conditions are presented in terms of simplified linear matrix inequalities (LMIs), which can be straightforwardly solved by Matlab. Finally, two simulation examples are provided to show the effectiveness and advantages of the proposed results.

Non-fragile [formula omitted] control for Markovian jump fuzzy systems with time-varying delays

This paper focuses on the non-fragile H∞ control of Markovian jump fuzzy systems with time-varying delays. In order to obtain less conservatism, an improved delay partitioning method is introduced, which divides the delay interval into multiple segments with a geometric sequence. A modified Lyapunov–Krasovskii functional is constructed and some less conservative delay-dependent stability criteria are derived by using linear matrix inequalities technique. Then a non-fragile controller is designed. Finally, two numerical examples are given to show the effectiveness of the obtained results.

A note on delay-dependent stability of Itô-type stochastic time-delay systems

Different from the existing delay-dependent stability criteria which depend on the size of the delays in both the drift and diffusion parts of stochastic time-delay systems (STDSs), this paper shows that the delay-dependent stability criterion depends only on the drift part and works for arbitrary large delays of the diffusion part of STDSs. By developing the stochastic version descriptor system approach, simple stability criterion is further derived for aperiodic sampled-data stochastic systems. The theoretical results are illustrated by means of a numerical example.

Exponential H ∞ output tracking control for coupled switched systems with states of different dimensions

This paper is concerned with the output tracking control for complex switched systems with non-diffusively delayed coupling. The states' dimensions are different in the coupled switched systems and reference system. On the base of the average dwell time and piecewise Lyapunov functional methods, a delay-dependent exponential stability criterion is derived for the switched systems under the QUAD condition which is less conservative than the Lipschitz condition. The state feedback controller is employed in the design of output tracking, and the tracking performance is guaranteed by solving a linear matrix inequality. Finally, three numerical examples are provided to show the advantage and effectiveness of the proposed theoretical results.

New Stochastic Stability Criteria for Nonlinear Neutral Markovian Jump Systems

This paper address the stochastic stability of neutral markovian jumping systems with nonlinear perturbations. By constructing novel Lyapunov functionals which contain an augmented Lyapunov functional, and combining with the new inequalities, new delay-dependent stochastic stability criteria for the nominal systems are obtained. The asymptotically stable condition is a special case for the stochastic stability condition as the systems without markovian jump. Numerical examples show that the derived conditions are much less conservative than those given in the existing literature.

Delay-dependent global exponential stability for neural networks with time-varying delay

This paper deals with the global exponential stability problem of neural networks with time-varying delay. A novel Lyapounov–Krasovskii functional (LKF), which contains a common double integral term, an augmented double integral term and two delay-product-type terms, is constructed to analyze the exponential stability. An auxiliary function-based integral inequality (AFBII) and two special forms of it are applied to estimate the upper bounds of single integral terms produced in the time derivation of the LKF candidate. By using the novel LKF and AFBII, some new cross terms of matrix variables are included in linear matrix inequalities (LMIs). As a result, a less conservative delay-dependent global exponential stability criterion is proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion.

Sampled-Data State Estimation for Neural Networks with Additive Time–Varying Delays

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampled-data control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen’s inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

Further Stability Analysis for Time-Delayed Neural Networks Based on an Augmented Lyapunov Functional

In this paper, the stability of time-delayed neural networks (DNN) is further analyzed. First, an augmented N-dependent Lyapunov-Krasovskii functional (LKF) is designed, where the non-integral terms are augmented with delay-dependent items and some additional state variables, and the integrated vector in the single-integral terms is also augmented by adding some integral interval-dependent items. The novel LKF complements some coupling information between the neuron activation function and other state variables. Second, a new delay-dependent stability criterion is proposed via the above LKF application. Third, in order to further demonstrate the advantages of the new LKF, two corollaries are also given under other simplistic LKFs. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach.