Bound Of Delay Research Articles

Scaled consensus for multi-agent systems with communication time delays

This paper aims to solve the scaled consensus problem of general linear multi-agent systems with non-uniform time-varying communication time-delay. The proposed consensus protocol is based on the low gain solution of a parametric algebraic Riccati equation. Based on the proposed consensus protocol, we obtain the sufficient condition for scaled consensus of multi-agent systems with communication time-delay. The results reveal that the upper bound of time-delay can be arbitrarily large if all poles of the system are zero. For the case of non-zero poles on the imaginary axis, the maximal admissible upper bound of the time-varying delay is provided. Simulation results are performed to demonstrate the scaled consensus performance of multi-agent systems.

Consensus for high-order multi-agent systems with communication delay

In this study, consensus problem for general high-order multi-agent systems with communication delay is investigated. Given the unstable agent dynamics and a known communication delay, two consensus protocols are designed to guarantee consensus over undirected network. By jointly researching the effects of agent dynamics and network topology, allowable delay bounds depending on the maxima of concave functions are easy to calculate. Especially, the maximum delay bound is derived when the network topology is completely connected. The main approach for the same involves designing the control gains on the basis of the solution of a parametric algebraic Riccati equation. Finally, the theoretical results are demonstrated via numerical simulations.

An improved reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay

This paper is concerned with stability of a linear system with a time-varying delay. First, an improved reciprocally convex inequality including some existing ones as its special cases is derived. Compared with an extended reciprocally convex inequality recently reported, the improved reciprocally convex inequality can provide a maximum lower bound with less slack matrix variables for some reciprocally convex combinations. Second, an augmented Lyapunov–Krasovskii functional is tailored for the use of a second-order Bessel–Legendre inequality. Third, a stability criterion is derived by employing the proposed reciprocally convex inequality and the augmented Lyapunov–Krasovskii functional. Finally, two well-studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time-varying delay than some existing criteria.

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.

Sampled-data state estimation for a class of delayed complex networks via intermittent transmission

This paper investigates the sampled-data state estimation problem for a class of delayed complex networks. At certain sampling times, transmission of sampled-data through communication network may fail, which means the considered estimator can only intermittently receive sampled-data. The main objective of this paper is to design a sampled-data state estimator subjected to intermittent transmission such that the error system is exponentially stable. Specifically, the error system is first transformed into time-varying delayed switched systems, including both stable and unstable subsystems. And then, to analyze the stability of the error system, a modified Halanay inequality is presented. In view of the modified Halanay inequality and switched systems methodology, a sufficient condition for globally exponential stability of the error system is established. Meanwhile, the upper bound of transmission failure rate is given, which reflects to be closely related to sampling period and the upper bound of node delays. Furthermore, the desired estimator gain of each node is explicitly provided by solving a set of matrix inequalities. Finally, a numerical simulation is carried out to verify the effectiveness of the inferred results.

EID estimator-based modified repetitive control for singular systems with time-varying delay

This paper investigates the disturbance rejection for a modified repetitive control system (MRCS) that is described by a class of linear singular systems in the presence of external disturbances and time-varying delay. In particular, an equivalent-input-disturbance (EID)-based estimator is included in the MRCS to compensate both periodic and aperiodic disturbances which yields an EID-based MRCS. More precisely, the incorporation of the EID-based estimator into the control input enables rejection of all types of disturbances in MRCS and tracking of a periodic reference input is archived via a repetitive controller. Attention is focused on the state-feedback repetitive controller design which not only guarantees the regular, impulse free, and asymptotic stability of the closed-loop singular MRCS, but also provides an optimized upper bound of the time-varying delay. Based on Lyapunov stability theory and utilizing some advanced mathematical techniques, a new set of delay-dependent sufficient conditions is presented in terms of linear matrix inequalities for obtaining the required result. Then, an explicit expression for the desired state-feedback repetitive control law is developed. Further, the obtained results are validated through two numerical examples in the simulation section.

Stability analysis of linear systems with an interval time-varying delay – A delay-range-partition approach

In this paper, the stability analysis problem of linear systems with an interval time-varying delay is investigated. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, which includes more information of the delay’s range and the delay’s derivative. Secondly, based on two improved integral inequalities which are less conservative than Jensen’s integral inequalities, a delay-range-partition (DRP) approach is proposed to estimate the upper bound of the derivative of the augmented Lyapunov-Krasovskii functional. Then, less conservative stability criteria in the form of linear matrix inequality (LMI) are established no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given, and their results are compared with the existing 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.

Comparison of bounding methods for stability analysis of systems with time-varying delays

Integral inequalities for quadratic functions play an important role in the derivation of delay-dependent stability criteria for linear time-delay systems. Based on the Jensen inequality, a reciprocally convex combination approach was introduced by Park et al. (2011) for deriving delay-dependent stability criterion, which achieves the same upper bound of the time-varying delay as the one on the use of the Moon’s et al. inequality. Recently, a new inequality called Wirtinger-based inequality that encompasses the Jensen inequality was proposed by Seuret and Gouaisbaut (2013) for the stability analysis of time-delay systems. In this paper, it is revealed that the reciprocally convex combination approach is effective only with the use of Jensen inequality. When the Jensen inequality is replaced by Wirtinger-based inequality, the Moon’s et al.inequality together with convex analysis can lead to less conservative stability conditions than the reciprocally convex combination inequality.Moreover, we prove that the feasibility of an LMI condition derived by the Moon’s et al.inequality as well as convex analysis implies the feasibility of an LMI condition induced by the reciprocally convex combination inequality.Finally, the efficiency of the methods is demonstrated by some numerical examples, even though the corresponding system with zero-delay as well as the system without the delayed term are not stable.

Exponential stability analysis and [formula omitted] synthesis of positive T-S fuzzy systems with time-varying delays

The α-exponential stability analysis and l1 controller synthesis of positive Takagi–Sugeno fuzzy discrete-time systems with time-varying delays are discussed in this paper. A sufficient condition of α-exponential stability for autonomous positive fuzzy systems is first established by constructing a new Lyapunov–Krasovskii functional, which depends on a given scalar 0<α<1 and the bound of time-varying delays. Then, a sufficient condition for controlled systems with l1 gain constraint is also presented while imposing α-exponential stability, upon which, a constrained l1 controller is designed for both single-input and multi-input cases. Finally, an example is given to show the feasibility of the theoretical results.

New result for generalized neural networks with additive time-varying delays using free-matrix-based integral inequality method

This paper investigates the problem of stability for generalized neural networks (GNNs) with additive time-varying delays. Different from previous literatures, a new augmented Lyapunov–Krasovskii functional (LKF) has been constructed. In this LKF, two augmented terms are constructed to establish the interaction among the state vectors with additive time delay upper bounds. In addition, in consideration of the information for two upper bounds, a single and a double integral terms which contain the two upper bounds of additive time-varying delays are firstly introduced to analyze the GNNs. So, based on those treatments, the information about upper bound of additive time-varying delays is sufficiently used. On the other hand, the free-matrix-based integral inequality which can deal with the time-varying delays directly is employed to bound the derivative of the LKF. Based on above works, less conservative criterion is finally derived. Numerical example is provided to show the effectiveness and less conservatism of the proposed results.

Lower Bound Analysis and Perturbation of Critical Path for Area-Time Efficient Multiple Constant Multiplications

In this paper, a precise systematic delay model is proposed for the analysis and estimation of critical path delay of multiple constant multiplication (MCM) blocks. For the first time in literature, the mathematical derivation of lower bound of critical path delay of MCM blocks is presented and necessary conditions for achieving the lower bound of critical path delay are discussed. It is shown that the lower bound of critical path delay of MCMs is significantly smaller than that achieved by existing MCM algorithms. An improved genetic algorithm-based approach, with a heuristic algorithm to generate the initial population, is proposed to search for low complexity MCM solutions with the lower bound of critical path delay. This is the first time that design algorithms with gate-level delay control is proposed. Moreover, it is shown that using the information of lower bound of critical path delay, perturbation of timing can be applied to tradeoff the lower bound critical path delay against hardware complexity. It is shown that area-time efficient design of MCM blocks can be obtained by using the proposed techniques.

Observer-Based Stabilization Control of Time-Delay T-S Fuzzy Systems via the Non-Uniform Delay Partitioning Approach

It is well known that intelligent control technology plays an important role in the design of many control systems, and intelligent control has aroused wide attention from scholars. Fuzzy control is also the case because fuzzy control is one branch of intelligent control. The Takagi-Sugeno (T-S) fuzzy model is an effective approach when dealing with complex nonlinear systems, and the advantages of fuzzy controller design is that the linear control methods can be used. In addition, nonlinearity and time delay are inherent and not all states are available in many practical system. Therefore, the observer-based stabilization control for time-delay T-S fuzzy systems is of great significance. With the help of the non-uniform delay partitioning approach, a novel method is put forward to analyze the stability of the time-delay T-S fuzzy system and design the observer-based feedback controller via the parallel distributed compensation (PDC) scheme. The sufficient conditions of asymptotic stability for both nominal and uncertain time-delay T-S fuzzy system are derived based on the Lyapunov stability theory and linear matrix inequality (LMI) techniques. What is more, the solving methods to obtain the controller gain matrices, observer gain matrices, and upper bound of time delay are presented. Two illustrative examples are given to demonstrate the effectiveness and verify the superiority of our developed methods. From the simulation results, it can be found that the most prominent advantages of our proposed methods lie on larger delay bound and less decision variables compared with other related methods. The problem of observer-based stabilization control for continuous nonlinear time-delay systems is investigated in this paper, and the delay-dependent stability criteria are derived to achieve greater delay bound by virtual of the non-uniform delay partitioning approach. Numerical examples further confirmed the effectiveness and advantages of our developed methods.

Flow Allocation for Maximum Throughput and Bounded Delay on Multiple Disjoint Paths for Random Access Wireless Multihop Networks

In this paper, we consider random access, wireless, multi-hop networks, with multi-packet reception capabilities, where multiple flows are forwarded to the gateways through node disjoint paths. We explore the issue of allocating flow on multiple paths, exhibiting both intra- and inter-path interference, in order to maximize average aggregate flow throughput (AAT) and also provide bounded packet delay. A distributed flow allocation scheme is proposed where allocation of flow on paths is formulated as an optimization problem. Through an illustrative topology it is shown that the corresponding problem is non-convex. Furthermore, a simple, but accurate model is employed for the average aggregate throughput achieved by all flows, that captures both intra- and inter-path interference through the SINR model. The proposed scheme is evaluated through Ns2 simulations of several random wireless scenarios. Simulation results reveal that, the model employed, accurately captures the AAT observed in the simulated scenarios, even when the assumption of saturated queues is removed. Simulation results also show that the proposed scheme achieves significantly higher AAT, for the vast majority of the wireless scenarios explored, than the following flow allocation schemes: one that assigns flows on paths on a round-robin fashion, one that optimally utilizes the best path only, and another one that assigns the maximum possible flow on each path. Finally, a variant of the proposed scheme is explored, where interference for each link is approximated by considering its dominant interfering nodes only.

Heterogeneous and Competitive Multiagent Networks: Couple-Group Consensus with Communication or Input Time Delays

This paper discusses the couple-group consensus problems for a class of heterogeneous multiagent networks including the following two cases: with communication and input time delays, respectively. Different from the related cooperative networks, two novel delayed group consensus protocols are designed based on the competitive relationship between the agents. Furthermore, we absolutely relax the in-degree balance and other restrictive preconditions which existed in the relevant works. Some sufficient algebraic criteria for the achievement of couple-group consensus and the upper bound of the input time delays are technically obtained via the frequency domain method and matrix theory, respectively. The results show that the achievement of the couple-group consensus depends on the second-order agents’ in-degree and the control parameters of the systems, whereas it is independent of the communication time delays. Meanwhile, the upper bound of the input time delay is determined by the control parameters and the in-degree of the first-order agents. Finally, the validity of the proposed results is verified by several simulated examples.

Synchronization Transition of Time Delayed Complex Dynamical Networks with Discontinuous Coupling**Supported by the National Natural Science Foundation of China under Grant No. 61681240393, and the Fundamental Research Funds for the Central Universities under Grant No. 2015XKMS076

This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.

Crowdsourced Mobile Data Transfer with Delay Bound

In this article, we design a crowdsourcing system, CrowdMAC, where mobile devices form a local community or marketplace to share network access and transfer data for each other. CrowdMAC enables (i) mobile clients to select and exploit multiple mobile hotspots in its vicinity for data transfer and (ii) mobile hotspots to open their cellular connectivity to admit/serve delay-bounded requests from mobile users for a fee. The evaluations of CrowdMAC indicate that (i) mobile clients can tune preferred trade-offs between cost and delay through a control knob, (ii) mobile hotspots comply with all delay bounds, and (iii) the system ensures stable and efficient transfer.

Delay analysis and optimization for inter-core interference in real-time embedded multicore systems

The Worst Case Execution Time (WCET) is one of the most important performance metrics in real-time systems. With multi-core architectures becoming a trend in real-time systems, the WCET analysis is of great challenge, since multiple cores accessing shared hardware resources, such as cache and bus, may result in significant interference on them. In this paper, we propose a finer grained approach to analyze the inter-core interference(bank conflict and bus access interference) on multi-core platforms with the interference-aware bus arbiter(IABA) and bank-column cache partitioning, and our approach can reasonably estimate interference delays based on request timing. Moreover, we optimize bank-to-core mapping to reduce the interference delays, and develop an algorithm for finding the best bank-to-core mapping. The experimental results show that our interference analysis approach can improve the tightness of interference delays by 18.36% on average compared to Upper Bound Delay(UBD) approach, and the optimized bank-to-core mapping can achieve the WCET improvement by 8.93% on average.

Leaderless and leader-following consensus of multi-agent chaotic systems with unknown time delays and switching topologies

In this paper the distributed consensus problem for a class of multi-agent chaotic systems with unknown time delays under switching topologies and directed intermittent communications is investigated. Each agent is modeled as a general nonlinear system including many chaotic systems with or without time delays. Based on the Lyapunov stability theory and graph theory, some sufficient conditions guarantee the exponential convergence. A graph-dependent Lyapunov proof provides the definite relationship among the bound of unknown time delays, the admissible communication rate and each possible topology duration. Moreover, the relationship reveals that these parameters have impacts on both the convergence speed and control cost. The case with leader-following communication graph is also addressed. Finally, simulation results verify the effectiveness of the proposed method.

Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties

This paper studies the stability conditions of a discrete-time switched linear system in the presence of affine parametric uncertainties and an unknown time delay. Based on a discrete Lyapunov functional, sufficient conditions are investigated to determine the upper bound of admissible time delay in the discrete-time switched system. Furthermore, the average dwell time method, which is an effective tool for stability analysis of switched systems, is used to derive the exponential stability conditions. These conditions characterize the switching signal, which does not depend on any uncertainties. Finally, numerical examples are provided to verify and compare the theoretical results.