Derivative Of Time-varying Delay Research Articles

Dynamic event-triggered-based global output feedback control for stochastic nonlinear systems with time-varying delay

The current study addresses the issue of global dynamic event-triggered control based on reduced-order observer for a class of nonstrict-feedback stochastic systems in the presence of time-varying delay. Firstly, a lemma about the variable separation technique is proposed and proved for dealing with nonlinear functions in stochastic time-delay systems, which avoids the restrictive growth assumption that nonlinear functions need to satisfy. Secondly, a reduced-order observer is devised to reconstruct partial unmeasured state variables in systems, which equilibrates the control behavior between output feedback and state feedback. Then, without imposing any constraints on the derivative of time-varying delay, a dynamic event-triggered controller based on the symbol function technique is constructed to reduce the waste of resources in data transmissions and improve the communication efficiency. Furthermore, in the light of the stability theory of stochastic systems and Lyapunov-Razumikhin lemma, it is proved that the designed control algorithm can ensure that the controlled system is globally asymptotically stable in probability. Finally, two simulation examples are provided to verify the effectiveness of the developed approach.

Formula omitted] master–slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control

This paper investigates the H∞ master–slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov–Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.

Adaptive Output Feedback Control for Stochastic Uncertain Nonlinear Time-Delay Systems

In this brief, the adaptive output feedback control problem for stochastic nonlinear time-delay systems with various uncertainties is considered. The unknown output function needs neither to be differentiable, that is, its derivative is limited to known/unknown upper and lower bounds, nor to guarantee its Lipschitz continuity. Besides, the upper bound on the derivative of time-varying delay and the growth rates of the nonlinear functions are proved to be not necessary. An adaptive output feedback control scheme is designed, in which a dynamic gain is embedded in the observer to dominate the time-varying delay and unknown growth rates, and a constant gain is embedded in the controller to dominate the unknown output function. It is proved that all signals of the closed-loop system are globally bounded almost surely and the bounds are ensured to be tuned by design parameters. Finally, a simulation is presented to show the validity of the control scheme.

Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

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.

Exponential Synchronization of Neural Networks With Time-Varying Delays via Dynamic Intermittent Output Feedback Control

This paper addresses the exponential synchronization problem for neural networks with time-varying delays. First, a novel controller is presented by combining intermittent control with dynamic output feedback control. Next, a sufficient criterion is established based on the Lyapunov-Krasovskii functional approach and the lower bound lemma for reciprocally convex technique to ensure exponential stability of the resultant closed-loop system. Then, some solvable conditions of the proposed control problem are derived in terms of linear matrix inequalities. Notably, our results here extend the existing ones to the relaxed case because the derivative of time-varying delays is now an arbitrary bounded real number. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed method.

State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties

This study examines the synchronization problem of impulsive neural networks with mixed time-varying delays and linear fractional uncertainties. The mixed time-varying delays include distributed leakage, discrete and distributed time-varying delays. Moreover, the restrictions on derivatives of time-varying delays with upper bounds to smaller than one is relaxed by introducing free weight matrices. Based on suitable Lyapunov–Krasovskii functionals and integral inequalities, linear matrix inequality approach is used to derive the sufficient conditions that guarantee the synchronization criteria of impulsive neural networks via delay dependent state feedback control. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Robust stochastic stability of power system with time-varying delay under Gaussian random perturbations

In this paper, by taking into account the stochastic perturbations, the power system with time-varying delay under Gaussian random perturbations is formulated into the stochastic differential equation, then the robust stochastic stability is discussed in detail. Based on Lyapunov stability theory, some improved robust stability and robust stochastic stability criteria are developed, where the restrictions on the derivative of time-varying delay are removed so as to reduce the conservatism. The obtained results formulated in the form of linear matrix inequalities (LMIs) can be effectively solved by the LMI toolbox. Finally, one machine and infinite system under random perturbations is provided to demonstrate the effectiveness and usefulness of the developed results.

Nonfragile RobustH∞Synchronization Approach for Drive-Response Complex Dynamical Networks with Randomly Occurring Controller Gain Fluctuations and Uncertainties

This paper investigates the nonfragileH∞synchronization problem of complex dynamical networks with randomly occurring controller gain fluctuations and uncertainties. These randomly occurring phenomena are described by independent stochastic variables satisfying Bernoulli distributions, which are adopted to model more realistic dynamical behaviors of the complex networks. By applying the Lyapunov-Krasovskii method, delay-dependent criteria are established to ensure that the synchronization can be achieved with the prescribedH∞disturbance attenuation. Moreover, the obtained results do not rely on the derivatives of time-varying delays. A set of nonfragile controllers are further designed in terms of linear matrix inequality (LMI) approach. Finally, a numerical example is given to illustrate the effectiveness of our theoretical results.

Exponential convergence analysis of uncertain genetic regulatory networks with time-varying delays

This study is concerned with the problem of exponential convergence of uncertain genetic regulatory networks with time-varying delays in the case of the unknown equilibrium point. The system׳s uncertainties are modeled as a structured linear fractional form. Novel stability criteria are obtained by using the lower bound lemma together with Jensen inequality lemma. In order to get rid of the rigorous constraint that the derivatives of time-varying delays must be less than one, a new approach is introduced by improving Lyapunov–Krasovskii functional rather than using the traditional free-weighting matrices. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

New Delay-Dependent Stability Criteria for Uncertain Neutral System with Time-Varying Delays and Nonlinear Perturbations

This study is concerned with the problem of robust stability analysis of uncertain neutral system with time-varying delays and nonlinear perturbations. The parameter uncertainties are modeled as a structured linear fractional form. By choosing an augmented novel Lyapunov---Krasovskii functional which contains some triple integral terms and using the lower bound lemma to handle the integral terms, less conservative criteria are obtained. Moreover, the rigorous constraint that the derivatives of time-varying delays must be less than one has been removed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Stochastic Stability of Genetic Regulatory Networks with Mixed Delays

In this paper, the asymptotical stability of stochastic genetic regulatory networks with time-varying delays and continuous distributed delays are investigated. The constraint that derivative of time-varying delays must be smaller than 1 is relaxed, and the activation functions are of more general descriptions, which generalize and improve the earlier methods. Based on the Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) techniques defined on convex set, stability criteria for stochastic delayed genetic regulatory networks are established in the form of LMIs, which can be easily verified. Numerical example is also given to demonstrate the effectiveness of the proposed criteria. Keywords: Distributed delays, Genetic regulatory network, Linear matrix inequality (LMI), Stochastic system, Time-varying delays.

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.

Delay-Dependent Robust Stability of Cellular Neural Networks with Time-Varying Discrete and Distributed Delay

Delay-dependent robust stability of neural networks with discrete and distributed delays is considered in this paper. Stability criteria are derived in LMIs avoiding bounding certain cross terms and the restriction of derivative of time-varying delay is removed. Numerical examples are given to indicate significant improvements over some existing results.

Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

Abstract In this paper, an improved mean-square exponential stability condition and delayed-state-feedback controller for stochastic Markovian jump systems with mode-dependent time-varying state delays are obtained. First, by constructing a modified Lyapunov-Krasovskii functional, a mean-square exponential stability condition for the above systems is presented in terms of linear matrix inequalities (LMIs). Here, the decay rate can be a finite positive constant in a range and the derivative of time-varying delays is only required to have an upper bound which is not required to be less than 1. Then, based on the proposed stability condition, a delayed-state-feedback controller is designed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Adaptive robust control of uncertain dynamical systems with multiple time-varying delays

The problem of adaptive robust stabilisation is considered for a class of dynamical systems with multiple time-varying delayed state perturbations, time-varying uncertain parameters, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties and external disturbances are unknown, and that the time-varying delays are any non-negative continuous and bounded functions. In particular, it is not required that the derivatives of time-varying delays have to be less than one. For such a class of uncertain time-delay systems, a new method is presented whereby a class of memoryless continuous adaptive robust state feedback controllers is proposed. By employing a quasi-Lyapunov function, it is shown that the solutions of uncertain time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed adaptive robust state feedback controllers are completely independent of time delays, the results obtained in the study may be also applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.

Sample-data Decentralized Reliable H∞ Hyperbolic Control for Uncertain Fuzzy Large-scale Systems with Time-varying Delay

This paper studies the problem of sampled-data reliable H ∞ hyperbolic control for uncertain continuous-time fuzzy large-scale systems with time-varying delay. Firstly, the fuzzy hyperbolic model (FHM) is used to establish the model for certain complex large-scale systems, then according to the Lyapunov direct method and the decentralized control theory of large-scale systems, linear matrixine qualities (LMIs)-based conditions arederived toguarantee the H ∞ performance not only when all control components are operating well, but also in the presence of some possible actuator failures. Moreover, the precise failure parameters of the actuators are not required, and the requirements are only the lower and upper bounds of failure parameters. The conditions are dependent on the upper bound of time-delay, and not dependent on the derivative of time-varying delay. Therefore, the obtained results are less conservative. Finally, two examples are provided to illustrate the design procedure and its effectiveness.

Robust stability of stochastic Cohen–Grossberg neural networks with mixed time-varying delays

In the paper, the problem of robust exponential stability analysis is investigated for stochastic Cohen–Grossberg neural networks with both interval time-varying and distributed time-varying delays. By employing an augmented Lyapunov–Krasovskii functional, together with the LMI approach and definition on convex set, two delay-dependent conditions guaranteeing the robust exponential stability (in the mean square sense) of addressed system are presented. Additionally, the activation functions are of more general descriptions and the derivative of time-varying delay being less than 1 is released, which generalize and further improve those earlier methods. Numerical examples are provided to demonstrate the effectiveness of proposed stability conditions.

Stability criteria for linear systems with multiple time-varying delays

New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature.