Upper Bound Of Time-varying Delay Research Articles

Consensus of Multiagent Systems With Time-Varying Delays and Switching Topologies Based on Delay-Product-Type Functionals.

This article investigates the consensus problem of multiagent systems (MASs) with time-varying delays subject to switching topologies. For the purpose of obtaining less conservative consensus conditions, first, a delay-product-type Lyapunov-Krasovskii functional (LKF) based on the auxiliary function-based integral inequality (AFBII) is constructed. Then, the generalized reciprocally convex matrix inequality (GRCMI) and a relaxed quadratic function negative-determination lemma are introduced to obtain the maximal-allowable upper bound of time-varying delays. Moreover, a proportional and derivative-like (PD-like) protocol is designed and the result is extended to the leader-following consensus of agents under Lipschitz nonlinear dynamics. Finally, two illustrative examples, including Chua's circuit, are given to demonstrate the advantages of the new consensus criteria.

Design and Analysis of Longitudinal Controller for the Platoon With Time-Varying Delay

The communication topologies between vehicles in a platoon substantially impact the platoon’s stability. This study provides a distributed linear feedback control law that considers time-varying delay with guaranteed internal and string stability of the platoon system under various communication topologies. Firstly, the vehicle dynamics linearized model was derived using the precise feedback linearization technology. Different types of communication topologies, such as vehicle-to-vehicle communication and sensor-based communication, were described using directed graphs. Secondly, the linear feedback control law was designed to establish the stable zone of the linear controller gain under the effect of different communication topologies using directed graphs and the Routh-Hurwitz stability theorem. The Lyapunov-Razumikhin theorem determines the upper bound of the time-varying delay of various communication topologies. Additionally, the string stability of leader-predecessor following topology was studied, and the results were combined with the internal stability to determine the upper bound of time-varying delay. Finally, the results were verified by conducting two numerical simulations.

Event-Triggered H∞ Load Frequency Control for Multi-Area Nonlinear Power Systems Based on Non-Fragile Proportional Integral Control Strategy

In this article, a new event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> load frequency control (LFC) approach with dynamic triggered algorithm (DTA) for multi-area nonlinear power systems (NPSs) based on non-fragile proportional integral control (NPI-control) strategy is addressed. Firstly, different from the existing linear single-area LFC model for power systems, an improved nonlinear multi-area model with the performance of large-scale adjustment frequency fluctuation is constructed by considering the phenomenon of overshoots and long-term oscillations. Due to the existence of control uncertainty, it is the first time that the NPI-control scheme is applied to LFC approach for NPSs. Then, the DTA is proposed to adjust the dynamic event-triggered parameters, which reduces the occupation of communication bandwidth and the data computation of NPSs. Furthermore, a modified quadratic form with time-varying matrix and two-side closed functional method are adopted to construct the relaxed Lyapunov-Krasovskii functional, where some slack matrices are unnecessarily positive definite. Based on Lyapunov method, some less-conservatism stability criteria are derived. Utilizing the linear matrix inequality toolbox, the allowable upper bound of time-varying delays and the NPI-controller are obtained. Finally, a numerical example is presented to demonstrate the availability of the approach developed in this work.

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.

Stochastic exponential stabilization of hybrid systems with time‐varying delays via adaptive control

The problem of stochastic stabilization for a class of hybrid dynamical systems with time-varying delays is investigated by adaptive control approach. An adaptive controller is designed to stabilize the hybrid systems, and a sufficient criterion for exponential stabilization is derived based on certain conditions. The time-varying delay observations on the states of noise are made and the least upper bound of time-varying delays is also obtained. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed new techniques.

New Results on Consensus of Multi-Agent Systems With Time-Varying Delays: A Cyclic Switching Technique

This paper studies the leader-following consensus problem of discrete-time multi-agent systems with time-varying delays by developing a new cyclic switching scheme. First, two delay-dependent cycle dwell time switching laws are proposed for the first time. Second, by the proposed cyclic switching laws and constructed Lyapunov functionals, new leader-following consensus criteria for discrete-time multi-agent systems with time-varying delays are derived in the form of linear matrix inequalities. Compared with the existing literature, the developed cyclic switching method not only greatly improves the upper bound of time-varying delays in the multi-agent system, but also gives the estimation of upper and lower bounds for dwell time of the system. Finally, some simulations for the leader-following consensus of multi-agent systems with time-varying delays are presented to verify the feasibility of the proposed scheme.

Non-fragile memory filtering of T-S fuzzy delayed neural networks based on switched fuzzy sampled-data control

This paper deals with the non-fragile memory filtering issue of T-S fuzzy delayed neural networks with randomly occurring time-varying parameters uncertainties and variable sampling rates. Compared with existing sampled-data control schemes, an improved switched fuzzy memory sampled-data control protocol is designed for the first time, which involves not only a signal transmission delay but also switched topologies. By developing some new terms and taking full advantage of the variable characteristics related to the actual sampling pattern, a modified loose-looped fuzzy membership functions (FMFs) dependent Lyapunov-Krasovskii functional (LKF) is constructed based on the information of the time derivative of FMFs. Meanwhile, some relaxed matrices chosen in LKF are not consequentially positive definite. Moreover, with the LKF methodology and employing the developed estimation technique, several optimized control algorithms with both a larger sampling period and upper bound of time-varying delays for achieving the stabilization of the resultant T-S fuzzy delayed neural networks are derived. Finally, a numerical example is presented to demonstrate the superiority and applicability of the theoretical results.

Finite-Time Stabilization for Discontinuous Interconnected Delayed Systems via Interval Type-2 T–S Fuzzy Model Approach

This paper investigates the finite-time stabilization for a class of interconnected systems with nonlinear discontinuous interconnections in which the time-varying delay are considered. By utilizing the universal approximation ability of the fuzzy model, a unified interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy-model-based interconnected delayed system is provided. Then, in order to solve the existence of solution for the concerned system with discontinuous right-hand side, the Filippov solutions are defined based on differential inclusion theory and set-valued analysis. Furthermore, by the IT2 T–S fuzzy model approach, a delayed state feedback controller equipped with discontinuous term and time-varying delays term is proposed. According to the classical finite time stability theory and generalized Lyapunov approach, finite-time stabilization for the discontinuous interconnected delayed system is achieved, and the estimate of settling time is given. Moreover, when the detailed information of time-varying delays is unknown, the finite-time stabilization is also realized via another improved controller, which only depends upon the upper bound of time-varying delays. Finally, the proposed methodologies are illustrated by a numerical example.

Fault‐tolerant SMC for Takagi–Sugeno fuzzy systems with time‐varying delay and actuator saturation

This study examines the problem of fault-tolerant sliding mode control (SMC) design subject to actuator saturation for a class of Takagi-Sugeno fuzzy systems with time-varying delay and external disturbances. Our main attention is to propose the fault-tolerant SMC such that for given any initial condition, the system trajectories are forced to reach the sliding surface within a finite time. On the basis of the SM surface and Lyapunov stability theorem, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established to not only guarantee the passivity and asymptotically stability of the resulting closed-loop system in the designed sliding surface, but also cover the issues of actuator saturation and performance constraints. Then, the desired gain matrix of the fault-tolerant SMC is obtained in respect of the previously established LMIs such that the reachability of the predefined sliding surface is ensured. It is worth pointing out that the obtained sufficient conditions can preserve the trade-off between the maximisation of admissible upper bound of time-varying delay and enlarging the estimation about the domain of attraction for the closed-loop system. Eventually, the effectiveness and robustness of the proposed control approach are demonstrated via simulation results.

Effects of leakage delays and impulsive control in dissipativity analysis of Takagi–Sugeno fuzzy neural networks with randomly occurring uncertainties

In this paper, dissipativity analysis problem is investigated for T-S fuzzy neural networks with leakage delays and impulsive effects. Sufficient conditions for the dissipativity criteria are derived by using Lyapunov–Krasovskii functional having triple and four integral terms with free weighting matrix method. The obtained results are dependent on the the leakage delay and upper bound of time-varying delay. Moreover, some comparisons are made to contrast to some of existing results about strictly (Q,S,R)−ϑ-dissipativity for the concerned neural networks. Finally, some numerical examples and their computer simulations are given to show the effectiveness of the proposed criteria.

Consensus of feedforward nonlinear systems with a time-varying communication delay

ABSTRACTThe consensus problem of feedforward nonlinear systems under an undirected network with a time-varying communication delay is studied. In order to solve this problem, new consensus controller with an additional design parameter that can eliminate the effect of a feedforward nonlinearity and a time-varying communication delay on the consensus problem is proposed. Also, it is proved that if an upper bound of time-varying delay is known, the proposed consensus controller can always solve the consensus problem of multi-agent systems even in the presence of feedforward nonlinearity and an arbitrarily large communication delay. A numerical example is given to illustrate the validness of the proposed approach.

Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies

Stochastic consensus problems for linear time-invariant multi-agent systems over Markovian switching networks with time-varying delays and topology uncertainties are dealt with. By using the linear matrix inequality method and the stability theory of Markovian jump linear system, we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the Markov process, provided the union of topologies associated with the positive recurrent states of the Markov process admits a spanning tree and the agent dynamics is stabilizable. Feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying delays. Numerical examples are given to show the feasibility of theoretical results.

Event-Triggered Average Consensus for Multiagent Systems with Time-Varying Delay

The paper investigates average consensus for multiagent systems with time-varying delay. A reducing dimension multiagent systems model is presented firstly. Using event-triggered mechanism to reduce network load, a comprehensive model is then proposed, which considers communication delay and triggered issue. Furthermore, the event-triggered average consensus stability of multiagent systems with fixed directed/undirected graph is analyzed, and sufficient conditions are provided. Moreover, the upper bound of time-varying delay can be obtained conveniently. Finally, simulation results confirm the feasibility and effectiveness of the proposed method.

Exponential state estimation for impulsive neural networks with time delay in the leakage term

In this paper, the exponential state estimation problem for impulsive neural networks with both leakage delay and time-varying delays is investigated. Several sufficient conditions which are given in terms of linear matrix inequalities (LMIs) are derived to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable by constructing suitable Lyapunov–Krasovskii functionals and employing available output measurements and LMI technique. The obtained results are dependent on the leakage delay and upper bound of time-varying delays and independent of the derivative of time-varying delays. Moreover, some comparisons are made to contrast to some of existing results about state estimation of neural networks. Finally, two numerical examples and their computer simulations are given to show the effectiveness of proposed estimator.

Robust stability criteria for uncertain neutral type stochastic system with Takagi–Sugeno fuzzy model and Markovian jumping parameters

In this paper, the robust stability for uncertain neutral stochastic system with Takagi–Sugeno (T–S) fuzzy model and Markovian jumping parameters (MJPs) are investigated. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. Some novel sufficient conditions are derived to guarantee the asymptotic stability of the equilibrium point in the mean square. By utilizing the Lyapunov–Krasovskii functional, stochastic analysis theory, some free weighting matrices and linear matrix inequality (LMI) technique, the upper bound of time-varying delay is obtained by using Matlab® control toolbox. Finally, some numerical examples are given to show the effectiveness of the obtained results.

Average Consensus in Networks of Multi-Agent with Multiple Time-Varying Delays

The average consensus in undirected networks of multi-agent with both fixed and switching topology coupling multiple time-varying delays is studied. By using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system and then LMI-based method can be applied conveniently. Convergence analysis is conducted by constructing Lyapunov-Krasovskii function. Sufficient conditions on average consensus problem with multiple time-varying delays in undirected networks are obtained via linear matrix inequality (LMI) techniques. In particular, the maximal admissible upper bound of time-varying delays can be easily obtained by solving several simple and feasible LMIs. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results.