Delay-dependent Robust Stability Research Articles

Robust delay-dependent stability of uncertain inertial neural networks with impulsive effects and distributed-delay

The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper. The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks. The robust distributed-delay-dependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities. Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance, but also be utilized to design the impulsive control for the uncertain inertial neural networks. The novel criteria complement and extend the previous works on uncertain inertial neural network with/without impulsive effects. Typical numerical examples are used to test the validity of the developed stability criteria finally.

Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we generalize the robust stability analysis of nonlinear stochastic time-delay systems to the uncertain neutral stochastic systems. Due to the added derivative term of time-delay, the proposed scheme can be applied more widely. Finally, numerical examples are provided to validate the derived results.

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.

Improved stability analysis and control design of reset systems

A reset methodology in controller design can affect the performance and stability of control systems. Stability of reset time delay systems can be addressed based on a similar theorem of Lyapunov-Krasoviskii theory. In this study, a robust delay-dependent stability analysis of reset control systems is proposed for linear time invariant case. The conditions of stability are given in terms of linear matrix inequalities. In addition, extension of results is given to investigate stability of non-linear reset systems. Numerical examples are used to illustrate the effectiveness of the proposed approaches.

Fuzzy sliding mode control design of Markovian jump systems with time-varying delay

This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique.

Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

This paper is concerned with the robust H∞ control problem of uncertain linear system with interval time-varying delays. Firstly, by using Wirtinger inequality approach, after constructing a new Lyapunov functional, the novel robust delay-dependent stability and stabilization criteria are developed. These improved results are expected to have less conservatism, due to the utilization of Wirtinger inequality and consideration of the information of the lower bound of time delay. Secondly, based on the obtained criteria, the memoryless H∞ state feedback controller design scheme is presented, thus robust H∞ controller design and performance analysis for uncertain linear system are developed. For a prescribed H∞ performance level, the designed robust H∞ controller can guarantee the uncertain linear system to be robustly stable and endure a larger delay. At last, numerical examples are provided to illustrate the effectiveness and superiority of the developed results.

Robust H∞ Control of Uncertain Stochastic Systems with Time-varying Interval Delays

A robust delay-dependent stability criterion for discrete-time uncertain stochastic systems is proposed to achieve asymptotical stability and H∞ performance in this paper. Based on modeling approaches, Linear Parameter Varying (LPV) system with multiplicative noise term is built to represent uncertain stochastic systems. Moreover, state and input delays are considered as two individual time-varying interval cases for general effect. Employing a novel Lyapunov-Krasovskii function, Jensen inequality and transform technology, some relaxed sufficient conditions are derived into Linear Matrix Inequality (LMI) forms to apply convex optimization algorithm. Through solving the derived conditions, Gain-Scheduled (GS) controller can be designed such that robust asymptotical stability and H∞ performance of closed-loop system are achieved in the mean square. At last, two numerical examples are provided to demonstrate applicability and effectiveness of this paper.

Delay-dependent robust stability analysis and stabilization of linear systems using a simple delay-discretization approach

In this paper, a discretization scheme is proposed for systems with constant delay and the delay is assumed to appear in range. The proposed approach uses simple Lyapunov-Krasovskii functional to derive the robust stability and stabilization criteria. As a result of which the derived criteria become finite-dimensional. Though the criteria give sufficient condition for stability, but they are less conservative than the existing results. To demonstrate the effectiveness of the approach, numerical examples are considered.

Delay Dependent Robust Stability of A Discrete Time Recurrent Neural Network with Time Varying Delays

In this paper, the robust stability analysis of a problem is investigated for a class of discrete recurrent neural networks with distributed time varying delays for delay dependent case. The problem is to determine the robust stability by employing Lyapunov–Krasovskii stability theory. The class of neural network under some consideration is globally asymptotically stable if the quadratic matrix inequality involving several parameters is less than zero. Furthermore, a Linear Matrix Inequality (LMI) approach is provided to show the stability analysis. The numerical examples are given to show the usefulness of the proposed robust stability conditions. The numerical simulation is proved using MATLAB.

Delay-dependent Robust Stabilization for Uncertain T-S Fuzzy Systems with Additive Time Varying Delays

Delay-dependent Robust Stabilization for Uncertain T-S Fuzzy Systems with Additive Time Varying Delays

Delay-dependent Robust Stabilization for Uncertain T-S Fuzzy Systems with Additive Time Varying Delays

This paper investigates the problem of robust stabilization for uncertain Takagi–Sugeno (T–S) fuzzy systems with additive time varying delays. An appropriate Lyapunov-Krasovskii function is considered for solving this problem, and obtains considerably less conservative results than existing methods. The proposed approach constructs a new Lyapunov-Krasovskii functional using two additive delay components, and no free weighting matrices are employed in the theoretical result derivation. This reduces the number of scalar decision variables in linear matrix inequalities. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method, and to allow comparison with previous works.

Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays

This paper is concerned with the robust absolute stability analysis for Lurie control of the neutral singular systems. By using Lyapunov–Krasovskii function method, delay dependent criteria for absolute stability of system are derived in terms of Linear Matrix Inequality. The difference between this paper and other existing results is that the lower bounds and upper bounds of discrete-delay are considered, which will obtain some less conservative stability analysis results. Finally, some numerical examples are presented to illustrate the effectiveness of the method.

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

Stability Analysis of Uncertain Temperature control system with two additive delays and nonlinear perturbation

In this paper, the problem of robust delay-dependent stability criterion is considered for a class of linear continuous time heat exchanger system with constant additive state-delays and bounded nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. In the proposed delay-dependent stability analysis, the time-delays are considered to be time-invariant. In the proposed delay-dependent stability analysis, a candidate LK functional is considered, and take the time-derivative of the functional is bounded using the Jenson integral inequality. The proposed stability analysis finally culminates into a stability criterion in LMI framework. The effectiveness of the proposed stability criterion is illustrated using a network controlled temperature control of heat exchanger system

New robust stability condition for discrete-time recurrent neural networks with time-varying delays and nonlinear perturbations

In this paper, the robust delay-dependent stability problem is investigated for discrete-time recurrent neural networks (DRNNs) with time-varying delays and nonlinear perturbations. A novel summation inequality is proposed, which takes information on the double summation of system state into consideration and further extends the discrete Wirtinger-based inequality. By utilizing technique of the novel inequality and Lyapunov–Krasovskii functionals, a sufficient condition on robust stability of DRNNs with time-varying delays and nonlinear perturbations is obtained in terms of linear matrix inequality. The numerical example is included to show that the proposed method is effective and provides less conservative results.

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.

Robust stabilization andH∞control of uncertain stochastic time-delay systems with nonlinear perturbation

Summary This paper investigates the problem of delay-dependent robust stochastic stabilization and H∞ control for uncertain stochastic nonlinear systems with time-varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H∞ control for uncertain stochastic system with time-varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed-loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.

Stability criterion for networked control systems with additive time-varying state-delays and bounded nonlinearity

In this paper, a robust delay-dependent stability criterion is presented for a class of networked control systems with additive time-varying state-delays and bounded nonlinear perturbations using Lyapunov-Krasovskii LK functional approach. In the proposed delay-dependent stability analysis, to reduce conservatism, a candidate LK functional is considered, and the time-derivative of the functional is bounded using reciprocal convex combination lemma. The proposed stability analysis eventually culminates into a stability criterion in LMI framework that can be solved readily using standard numerical packages. The effectiveness of the proposed stability criterion is illustrated using a standard numerical example and a network controlled DC servo system.

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.

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.