Fast Time-varying Delays Research Articles

Adaptive fuzzy output-Feedback control of switched large-Scale systems with fast time-Varying delay

In this paper, an adaptive fuzzy decentralized output-feedback control is developed for the uncertain switched large-scale interconnected nonlinear system, which contains fast time-varying delays and unknown nonconstant control coefficients. By introducing and proving a new lemma, an improved analysis method is given based on the Lyapunov-Krasovskii (LK) functional, and it gets rid of the dependence of LK functional design on the bound of the derivative of the delay. Immeasurable states are estimated by co-designing the decentralized state observer and the innovative compensation system, which eliminates a widely adopted but strict assumption that the unknown control coefficient must be constant. By comprehensively designing the state observer, the compensation system and LK functionals, a novel adaptive fuzzy decentralized output-feedback control law is proposed, and stability of the closed-loop system is guaranteed theoretically based on an improved average dwell time. Finally, the effectiveness is further verified by complete simulation experiments.

Finite time SF bifurcation and stability analysis for stochastic time-varying delay system

In this paper, it is found that the systems alternate between oscillatory and steady states in studying the stability of a class of stochastic dynamical systems with fast time-varying periodic delays. We propose a new definition of bifurcation, State Flip (SF) bifurcation, by using the abrupt change in the dwell time ratio of two states. Taking the amplitude of the time-varying delay function δ as the bifurcation parameter, we investigate the dynamics of the evolution of a time-varying delay system driven by Gaussian white noise. Firstly, we convert systems with fast time-varying periodic delays into comparative systems with distributed delays, which in turn are converted into stochastic systems with constant delays for discussion. In order to reduce the stochastic delay equation to the average Itô equation, we adopted the stochastic averaging method and the generalized central manifold theory. It is used to capture the one-dimensional slow variables of a system near the critical state of the transition between two steady states during the evolution of the system. We then find that as the amplitude increases from weak to strong, the stochastic time-varying delay system changes from a two-period oscillation to alternating between oscillation and steady, and finally to a steady state. Lastly, we perform numerical simulations of the original stochastic time-varying delay system and the transformed two-dimensional stochastic constant time-delay system respectively to verify that the ideas and methods in this paper are reasonable and effective.

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.

Fault diagnosis and fault-tolerant control for system with fast time-varying delay

This paper proposes a fault diagnosis and fault-tolerant control method for a system with a fast time-varying delay and time-varying parameters. A fault observer is designed to estimate faults, and an improved fast adaptive fault estimation (FAFE) algorithm is developed to reduce the relevant constraints in the general form of this algorithm. With newly introduced relaxation matrices, this study estimates faults in a system exhibiting a fast time-varying delay. Based on the estimated faults, an output feedback controller is designed to accommodate the faults. The fault-tolerant control is realized using the introduced relaxation matrices. An algorithm is derived to solve for the observer and controller. Finally, the theory and method are validated using a real example of a helicopter system.

Robust stability analysis of formation control in local frames under time-varying delays and actuator faults

This paper investigates the robust stability of a multiagent system moving to a desired rigid formation in presence of unknown time-varying communication delays and actuator faults. Each agent uses relative position measurements to implement the proposed control method, which does not require common coordinate references. However, the presence of time delays in the measurements, which is inherent to the communication links between agents, has a negative impact in the control system performance leading, in some cases, to instability. Furthermore, the robust stability analysis becomes more complex if failures on actuators are taken into account. In addition, delays may be subject to time variations, depending on network load, availability of communication resources, dynamic routing protocols, or other environmental conditions. To cope with these problems, a sufficient condition based on Linear Matrix Inequalities (LMI) is provided to ensure the robust asymptotic convergence of the agents to the desired formation. This condition is valid for any arbitrarily fast time-varying delays and actuator faults, given a worst-case point-to-point delay. Finally, simulation results show the performance of the proposed approach.

Distributed optimisation problem with communication delay and external disturbance

ABSTRACTThis paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov–Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method.

A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.

Further Results on Stability Analysis for Markovian Jump Systems with Time-Varying Delays

This paper is concerned with the problem of stability analysis for Markovian jump systems with time-varying delays. By constructing a newly augmented Lyapunov-Krasovskii functional and combining Wirtinger-based integral inequality, an improved delay-dependent stability criterion within the framework of linear matrix inequalities (LMIs) is introduced. Based on the result of delay-dependent stability criterion, when linear systems have fast time-varying delays, a corresponding stability condition is given. Via three numerical examples, the improvements of the proposed criteria are shown by comparing maximum delay bounds provided by our theorems with the recent results.

Analysis on Global Asymptotical Stability of Genetic Regulatory Networks with Time-Varying Delays via Convex Combination Method

The global asymptotical stability analysis for genetic regulatory networks with time delays is concerned. By using Lyapunov functional theorem, LMIs, and convex combination method, a new delay-dependent stability criterion has been presented in terms of LMIs to guarantee the delayed genetic regulatory networks to be asymptotically stable. The restriction that the derivatives of the time-varying delays are less than one is removed. Our result is applicable to both fast and slow time-varying delays. The stability criterion has less conservative and wider application range. Experimental result has been used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.

Stability of Genetic Regulatory Networks with Interval Time-Varying Delays via Convex Combination Method

In this paper, asymptotical stability of genetic regulatory networks with interval time-varying delays is investigated. By choosing an appropriate new Lyapunov functional and employing convex combination method to estimate the derivative of the Lyapunov functional, some new delay-range-dependent and delay-derivative-dependent/independent stability criteria are presented in terms of linear matrix inequalities (LMIs). The important feature is that the obtained stability criteria are applicable to both fast and slow time-varying delays due to the ranges for the time-varying delays have been carefully considered. Three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the presented results

Robust Stability Analysis for T-S Fuzzy Neural Networks with Time-varying Delays

In this paper, the robust stability of T-S fuzzy uncertain system for neural networks with time-varying delays is investigated. The constraint on the time-varying delay function is removed, which means that a fast time-varying delay is allowed. Based on the Lyapunov- Krasovskii functional techniques and integral inequality approach (IIA), novel robust stability criteria have been derived in terms of linear matrix inequalities which can be easily solved using the efficient convex optimization algorithm. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov-Krasovskii functional. Examples are included to illustrate our results. These results are shown to be less conservative than those reported in the literature.

Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov-Krasovskii functional method.

This paper is concerned with the synchronization problems for an array of neural networks with hybrid coupling and interval time-varying delay. First, a novel augmented Lyapunov-Krasovskii functional (LKF) method is proposed to develop delay-dependent synchronization criteria for the networks, which makes use of more relaxed conditions by employing the new type of augmented matrices with Kronecker product operation. The proposed method can handle a multitude of Kronecker product operations in the LKF and alleviates the requirements of the positive definiteness of some conditional matrices which are usually considered in the existing methods for complex networks. This leads to a significant improvement in the performance of the synchronization criteria, i.e., less conservative synchronization results can be obtained. Meanwhile, the case of fast time-varying delay can also be handled by the proposed method. Furthermore, based on the derived criteria, a robust synchronization criterion is obtained for the system with uncertainties both in coefficient and coupling matrix terms. Since an expression based on linear matrix inequality is used, the proposed criteria can be easily checked in practice. Finally, numerical examples are provided to show the effectiveness of the proposed method.

State estimation of recurrent neural networks with interval time-varying delay: an improved delay-dependent approach

This paper is concerned with the state estimation problem for a class of recurrent neural networks with interval time-varying delay, where time delay includes either slow or fast time-varying delay. A novel delay-dependent criterion, in which the rate–range of time delay is also considered, is established to estimate the neuron states through available output measurements such that, for all admissible time delays, the dynamics of the estimation error system is globally asymptotically stable. The proposed method is based on a new Lyapunov–Krasovskii functional with triple-integral terms and free-weighting matrix approach. Numerical examples are given to illustrate the effectiveness of the method.

Design of control strategies for robust dynamic routing in traffic networks

In this study, improved centralised and decentralised routing control strategies are developed based on minimisation of the worst-case queuing length. The centralised routing problem is formulated as an ℋ∞ optimal control problem to achieve a robust routing performance in the presence of unknown fast time-varying network delays. Then a decentralised routing problem is reformulated by treating every node as a single subsystem thereby yielding an algorithm that obtains the fastest route. In both cases, unconstrained solution is derived to design a delay-dependent ℋ∞ controller and expressed in terms of the feasibility of linear matrix inequality (LMI). Subsequently, physical constraints are imposed and added as LMIs. Salient features of the developed routing methodology including the increase of robustness against multiple unknown time-varying delays, and the enhancement of the scalability of the algorithm to large-scale traffic networks are delineated. Simulation results are presented to demonstrate the effectiveness and capabilities of the developed dynamic routing strategies.

On delayed uncertain genetic regulatory networks: robust stability analysis

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.

Improved robust stability criteria for neural networks with fast time-varying delays

An improved robust global stability criterion is developed for uncertain neural networks with fast time-varying delays. The networks have norm-bounded parametric uncertainties. The relationship between the time-varying delay and associated extreme bounds (lower and upper) is appropriately exploited when dealing with the Lyapunov functional derivative. The developed stability criterion is delay dependent and is characterized by linear-matrix-inequality-based conditions. Numerical examples are presented to illustrate the benefits and lower conservativeness of the developed method.

Novel robust exponential stability criteria for neural networks

This paper investigates the problem of robust global exponential stability analysis for uncertain neural networks with interval time-varying delays. The time-delay pattern is quite general and including fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. The activation functions are monotone nondecreasing with known lower and upper bounds. Novel stability criteria are developed by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs)-based conditions. The developed stability results are less conservative than previous published ones in the literature, which is illustrated by a representative numerical example.

Improved delay-dependent stability criterion for uncertain networked control systems with induced time-varying delays

In this paper, a new stability criterion for uncertain systems controlled over a communication network is derived. Bounds on the network induced time-varying delays are assumed to be known, and no restriction on the derivative of the time-varying delay is imposed allowing for fast time-varying delay profiles. Both, L2-bounded disturbances and norm-bounded, possibly time-varying, uncertainties are considered. Stability conditions are obtained based on the Lyapunov-Krasovskii approach, considering a new treatment of time-varying delays resorting to a polytopic covering of the delay interval. Examples are provided to demonstrate the reduced conservatism of the proposed conditions with respect to available works in the literature.

New exponentially convergent state estimation method for delayed neural networks

The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example.