Delay-dependent Robust Stability Criteria Research Articles

System decomposition-based stability criteria for Takagi-Sugeno fuzzy uncertain stochastic delayed neural networks in quaternion field

<abstract><p>Stochastic disturbances often occur in real-world systems which can lead to undesirable system dynamics. Therefore, it is necessary to investigate stochastic disturbances in neural network modeling. As such, this paper examines the stability problem for Takagi-Sugeno fuzzy uncertain quaternion-valued stochastic neural networks. By applying Takagi-Sugeno fuzzy models and stochastic analysis, we first consider a general form of Takagi-Sugeno fuzzy uncertain quaternion-valued stochastic neural networks with time-varying delays. Then, by constructing suitable Lyapunov-Krasovskii functional, we present new delay-dependent robust and global asymptotic stability criteria for the considered networks. Furthermore, we present our results in terms of real-valued linear matrix inequalities that can be solved in MATLAB LMI toolbox. Finally, two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.</p></abstract>

Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems

In this paper, the robust stability and stabilization problems for fractional-order time-varying delay systems are investigated. Firstly, a new fractional-order Razumikhin theorem is given. By using the proposed fractional-order Razumikhin theorem, novel delay-dependent stability conditions for both nominal and uncertain linear fractional-order time-varying delay systems are derived. The results are in form of linear matrix inequalities, which are convenient for application and calculation. Then, the obtained stability conditions are utilized to derive a state feedback stabilization controller. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, three examples are provided to illustrate that the proposed results are valid and less conservative.

Further Robust Stability Analysis For Time-delayed Neutral-type Systems by a Modified Lyapunov-Krasovskii Functional

This paper further studies the stability of the uncertain delayed neutral-type system by constructing a novel Lyapunov-Krasovskii functional (LKF) with some delay-dependent and N-dependent items. Some new delay-dependent robust stability criteria are proposed based on linear matrix inequality (LMI). The criteria proposed in this paper are less conservative than some recent previous ones. Some numerical examples, including a linear neutral-type system, the partial element equivalent circuit and a general linear system, are presented to show the effectiveness of the proposed approach.

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

New delay-dependent robust exponential stability for uncertain linear systems with multiple non-differentiable time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability analysis for uncertain linear systems with constant delay, time-varying delay and nonlinear perturbations. The restriction on the derivative of time-varying delay is removed, which means that the fast time-varying delays are allowed. Combined with Leibniz-Newton formula, integral inequalities, Wirtinger-based integral inequality, Peng-Park’s integral inequality, utilization of zero equation and new Lyapunov-Krasovskii functional have been adopted to study. New delay-dependent robust stability criteria for uncertain time-delay systems are established in terms of linear matrix inequalities (LMIs). Numerical examples and simulation suggest that the results given to illustrate the effectiveness and improvement over some existing methods.

Delay-dependent robust stability criteria for singular time-delay systems by delay-partitioning approach

ABSTRACTIn this paper, the problem of delay-dependent robust stability for singular time-delay systems is investigated. The parametric uncertainties are assumed to be norm bounded. Based on the idea of delay partitioning, A new Lyapunov–Krasovskii functional is proposed to develop new delay-dependent criteria, that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, some numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous works.

Novel delay-dependent robust stability criteria for neutral-type time-varying uncertain Lurie nonlinear control system with mixed time delays

Novel delay-dependent robust stability criteria for neutral-type time-varying uncertain Lurie nonlinear control system with mixed time delays

Neural-network based approach on delay-dependent robust stability criteria for dithered chaotic systems with multiple time-delay

A novel approach is proposed in this study to eliminate the chaotic motion by a fuzzy controller and an appropriate dither. First, a back-propagation (BP) neural-network (NN) model is used to approximate the multiple time-delay chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on the LDI state-space representation, this study proposes a delay-dependent stability criterion derived in terms of Lyapunov’s direct method to guarantee that the trajectories of the multiple time-delay chaotic (MTDC) system under fuzzy control can be steered into a periodic orbit. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is then synthesized to tame the multiple time-delay chaotic (MTDC) system. If the fuzzy controller cannot suppress the chaos, a high frequency signal, commonly called dither, is simultaneously injected to eliminate the chaotic motion by regulating the dither’s parameters. If the frequency of dither is high enough, the trajectories of the dithered chaotic system and its corresponding mathematical model-the relaxed system can be made as close as desired. This make it possible to obtain a rigorous prediction of the dithered chaotic system’s behavior by establishing the relaxed system. Finally, this study provides a numerical example of the Chen’s chaotic system with simulations to illustrate the concepts discussed throughout this paper.

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

An improved robust stability analysis for systems with two delays by extracting overlapping feature

In this paper, a delay-dependent robust stability criterion is proposed for linear systems with two delays. For delay-dependent stable systems, the delays are very small in nature. So, they may overlap each other. This overlapping information may be exploited to obtain a less conservative criterion. To extract such information, a special type of simple Lyapunov–Krasovskii functional is considered. To derive the criterion in form of Linear Matrix inequalities, a matrix variable approach is used. Some numerical examples are presented to validate the less conservativeness of the proposed criterion.

Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays

This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to be m in number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov–Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods.

Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays

This paper is concerned with the problem of improved delay-dependent robust stability criteria for neutral-type recurrent neural networks (NRNNs) with time-varying delays. Combining the Lyapunov–Krasovskii functional with linear matrix inequality (LMI) techniques and integral inequality approach (IIA), delay-dependent robust stability conditions for RNNs with time-varying delay, expressed in terms of quadratic forms of state and LMI, are derived. The proposed methods contain the least number of computed variables while maintaining the effectiveness of the robust stability conditions. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

On improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K 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 optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Delay-dependent robust stability criteria for stochastic neural networks of neutral-type with interval time-varying delay and linear fractional uncertainties

In this paper, we investigate the problem of robust stability for a class of delayed neural networks of neutral-type with linear fractional uncertainties. The activation functions are assumed to be unbounded, non-monotonic and non-differentiable, and the delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of the interval time-varying delay are available. By constructing a general form of the Lyapunov–Krasovskii functional, and using the linear matrix inequality (LMI) approach, we derive several delay-dependent stability criteria in terms of LMI. Finally, we give a number of examples to illustrate the effectiveness of the proposed method.

Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching.

This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Improved Results on Robust Stability for Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigated delay-dependent robust stability criteria for systems with interval time-varying delays and nonlinear perturbations. A delay-partitioning approach is used in this paper, the delay-interval is partitioned into multiple equidistant subintervals, a new Lyapunov-Krasovskii (L-K) functional contains some triple-integral terms, and augment terms are introduced on these intervals. Then, by using integral inequalities method together with free-weighting matrix approach, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper investigates the problem of robust stability for neutral type system with mixed delays and time-varying structured uncertainties. Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method, some new stability criteria are presented. The difference between this paper and other existing results is that the lower bounds and upper bounds of the neutral-delay and discrete-delay are considered, which will obtain some less conservative stability analysis results. Several numerical examples are given to demonstrate the effectiveness and merit of the proposed results.

New delay dependent robust stability criteria for T-S fuzzy systems with constant delay

This paper deals with the problem of delay dependent robust stability for T-S fuzzy time delay systems. The approach based on constructing a new Lyapunov-Krasovskii functional by dividing uniformly the delay interval into N segment with N is positive integer, and using Finsler’s lemma. This new Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments. The perturbations considered are norm bounded, and the results are expressed in terms of linear matrix inequality (LMIs). Numerical examples are provided to show the effectiveness of the present method, compared with some recent previous ones.

On exponential stabilization for a class of neutral-type systems with parameter uncertainties: An integral sliding mode approach

This paper is focused on integral sliding mode control (ISMC) for a class of parameter uncertain neutral-type systems with time-varying delays (NTSTD). An integral sliding surface functional is firstly constructed for the NTSTD. Then, a delay-dependent robust stability criterion is established for all admissible uncertainties, which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate. In addition, by solving the generalized eigenvalue problem (GEVP) presented in the subsequent work, the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived. Furthermore, a sliding mode control (SMC) law is then synthesised to ensure the stability of the closed-loop system, and the proposed SMC law can drive the state of controlled dynamic system into the predefined sliding surface in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results.