Cases Of Time-varying Delays Research Articles

Neural network-based robust consensus tracking for uncertain networked Euler-Lagrange systems with time-varying delays and output constraints

This paper mainly focuses on the cooperative robust consensus tracking problem of uncertain networked Euler-Lagrange systems (NELSs) with time-varying delays and output constraints. By systematically integrating the neural network (NN) adaptive technique and the logarithmic type Barrier Lyapunov Function (BLF) in combination with the additional robust control law, two distributed robust consensus schemes for uncertain NELSs are proposed for two cases of time-varying communication and input delays respectively, which can fully guarantee to constrain the output consensus error within a safety region simultaneously. Furthermore, numerical simulation examples are provided to demonstrate the comparable potential advantages of the proposed robust control law over some existing algorithms, including adaptability, stability, and robustness, as well as delay effects.

Stability of Delay Hopfield Neural Networks with Generalized Riemann-Liouville Type Fractional Derivative.

The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann-Liouville fractional derivative (GRLFD) with an exponential kernel. The kernels of the fractional integral and the fractional derivative in this paper are Sonine kernels and satisfy the first and the second fundamental theorems in calculus. The presence of delays and GRLFD in the model require a special type of initial condition. The applied GRLFD also requires a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. An inequality for Lyapunov type of convex functions with the applied GRLFD is proved. It is combined with the Razumikhin method to study stability properties of the equilibrium of the model. As a partial case we apply quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included.

Stability of delay Hopfield neural networks with generalized proportional Riemann-Liouville fractional derivative

<abstract><p>The general delay Hopfield neural network is studied. It is considered the case of time-varying delay, continuously distributed delays, time varying coefficients and a special type of a Riemann-Liouville fractional derivative (GPRLFD) with an exponential kernel. The presence of delays and GPRLFD in the model require two special types of initial conditions. The applied GPRLFD also required a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. We use Razumikhin method and Lyapunov functions to study stability properties of the equilibrium of the model. We apply Lyapunov functions defined by absolute values as well as quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GPRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included.</p></abstract>

Cloud-based Connected Vehicle Control under Time-Varying Delay: Stability Analysis and Controller Synthesis

The emergence of connected vehicles and cloud-based control technologies promise great benefits to transportation systems. For practical application, time-varying delay from vehicular communication and edge/cloud computing has a critical influence on the vehicle control performance. To address this problem, this paper focuses on the stability analysis and controller design for connected vehicles under time-varying delay at the cloud-based control architecture. Particularly, connected car-following control and connected path-following control are under consideration as specific examples, where the cloud-unit assigns the control commands. A general switched system model has been established for connected vehicle control, where time-varying delay is imposed on partial system states. For stability analysis, an improved stability condition is proposed for the switched system under general case of time-varying delay with less conservative property compared with existing work. Further, based on Markov process assumption on time-varying delay, a quantitative stability evaluation method is introduced. Then, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> controller design method has been presented, which incorporates multiple requirements, including stability under delay, control error for safety, and control rapidity. Extensive numerical simulations validate the performance of the proposed control method at multiple traffic scenarios.

Global Stabilization for a Class of Switched Nonlinear Time-Delay Systems via Sampled-Data Output-Feedback Control

This article presents a stabilization achievement for a switched nonlinear time-delay system through output-feedback control under the sampled-data and global senses. An observer with the sampled output measurement is constructed to evaluate the unavailable states, and then a controller formed from the sampled observer states is given. For the stability analysis, a merging virtual switching signal (MVSS) is created to express the asynchronous switching mechanism in the resultant closed-loop system. Through designating a positive-definite function as the Lyapunov function candidate, a proof is conducted to reveal that global stability can be ensured for the considered systems which work under the time-varying delay case and the developed sampled-data controller with a switching restriction. Finally, two examples are provided in this article to indicate the given control strategy usefulness.

Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

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.

Stability Analysis for the Discrete-Time T-S Fuzzy System with Stochastic Disturbance and State Delay

In this paper, we study the stability for discrete-time Takagi and Sugeno (T-S) fuzzy systems with perturbation disturbance and time delay. Stochastic delay-dependent stability criteria are derived for stochastic T-S fuzzy systems with time-invariant and time-varying delays, respectively. For the time-varying delay case, a novel fuzzy Lyapunov–Krasovskii functional (LKF) without requiring all the involved symmetric matrices to be positive definite is constructed to reduce the conservatism. These stability conditions are then represented in terms of finite linear matrix inequalities (LMIs), which can be solved efficiently by using standard LMIS optimisation techniques. Two numerical examples are given to illustrate the feasibility of the proposed method.

Exponential stability analysis for singular switched positive systems under dwell-time constraints

The article addresses the exponential stability analysis for singular switched positive systems(SSPSs) under dwell-time constraints which include mode-dependent minimum dwell time(MDMDT), mode-dependent constant dwell time(MDCDT) and mode-dependent ranged dwell time(MDRDT) constraints. For SSPSs in both delay-free case and time-varying delay case, a sufficient exponential stability condition is proposed with MDMDT, MDCDT and MDRDT constraints, respectively, and the exponential decay rate can be set as a free parameter based on diverse circumstances. To analyze the dwell-time stability, a novel discretized linear copositive Lyapunov function(DLCLF) approach is introduced in the article, and compared with the general copositive and homogeneous Lyapunov function approach, the main advantage of the DLCLF technique is itself affine dependence on conditions of system matrix, which will be extended and utilized to systems with uncertainties or/and time-varying parameters quite easily. Meanwhile, the proposed condition of exponential stability under MDMDT(or MDCDT or MDRDT) constraint will be degenerated into the one under minimum dwell time(or constant dwell time or ranged dwell time) constraint for some specific situations, which implies that the considered MDMDT(or MDCDT or MDRDT) case is more general and practical. Finally, the validity and significance of the results are illustrated by seven examples.

Second-order bipartite consensus for networked robotic systems with quantized-data interactions and time-varying transmission delays

This paper investigates the second-order bipartite consensus (BC) problems for networked robotic systems (NRSs) subject to model uncertainties and external disturbances over signed directed graphs. We have newly presented two classes of hierarchical control algorithms (HCAs) to solve the BC problems for NRSs in a more practical and challenging case of quantized-data interactions (QDIs) and time-varying transmission delays (TVTDs). By using Hurwitz criterion and Lyapunov stability argument, several sufficient conditions on control parameters are obtained and the BC performance of the regulated system is analyzed. Three examples validate the presented theoretical findings.

Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality

This paper focuses on stability analysis of linear systems with time-varying delay, where two cases of the time-varying delay are discussed, that is, the time-varying delay is either differentiable or just uniformly continuous. First, an improved triple-integral inequality is proposed to estimate triple-integrals tightly. Then, by introducing two novel Lyapunov–Krasovskii functionals catering for two cases of time-varying delay, two sufficient conditions on stability, respectively, for the system under two cases of time-varying delay are derived using the improved triple-integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently. Finally, three numerical examples show that the obtained results outperform some existing ones.

Interval matrix method based synchronization criteria for fractional-order memristive neural networks with multiple time-varying delays

This paper addresses the issue of globally asymptotical synchronization of fractional-order memristive neural networks (FMNNs) with multiple time-varying delays. First, a more practical model for FMNNs with multiple time-varying delays is proposed because of considering the characteristics of a real memristor. Under the framework of differential inclusions, the FMNN is transformed into a fractional-order neural network (FNN) with interval uncertainties. Thus, the synchronization of two FMNNs is converted into the synchronization of two FNNs with interval parameters. The main problems to overcome are: (1) establishing an effective differential inequality for fractional-order systems with multiple time-varying delays; (2) finding a better upper bound for the norm of interval matrices. In this paper, a new upper bound for the norm of interval matrices is derived and meanwhile the fractional Halanay inequality is generalized to the case of multiple time-varying delays. Then, synchronization control strategies are elaborately designed to achieve globally asymptotical synchronization. By exploiting the newly-built fractional Halanay inequality and constructing appropriate Lyapunov functions, some new sufficient conditions for globally asymptotical synchronization of FMNNs with time-varying delays are derived. The synchronization criteria, expressed by LMIs, are easy to check and extend some previously published results. An illustrative numerical example is given to demonstrate the effectiveness of the theoretical results.

Discrete-Time Systems With Constrained Time Delays and Delay-Dependent Lyapunov Functions

It is proved in this paper that the existence of a delay-dependent suitable Lyapunov function is a necessary and sufficient condition for a discrete-time fully nonlinear time-delay system, with given delays digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the delays digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. The case of arbitrary time-varying time delays, with no constraints as long as bounded, is covered as a special case.

Leader–Follower Consensus Control of Multiple Quadcopters Under Communication Delays

This paper develops a novel decentralized leader–follower consensus algorithm for multiple-quadcopter systems under uniform constant and asynchronous time-varying communication delays. The consensus problem is formulated as the stability analysis and static controller design problem of a delayed system by defining the consensus error dynamics. Lyapunov-based methods along with the linear matrix inequality (LMI) techniques are utilized to derive the sufficient conditions for the control gain design that ensure asymptotic consensusability in the constant delay case, and consensus with bounded errors in the time-varying delay case. Also the computational complexity of solving control gains can be significantly reduced by decomposing the sufficient conditions into a set of equivalent low-dimensional conditions under undirected communication topologies. Simulation results show that larger systems are generally more susceptible to communication delays, and systems are more robust to delays when more followers are directly connected to the leader.

Observer design for a class of disturbed nonlinear systems with time-varying delayed outputs using mixed time-continuous and sampled measurements

A state observer is proposed for a class of uniformly observable systems involving bounded disturbances. The system outputs are delayed with a known (time-varying) delay and their measurements are continuously available over some time horizons and sampled over other ones. The rational behind the proposed observer design consists in the consideration of an appropriate corrective term provided by a linear Delay Differential Equation (DDE), which accounts for the form under which the output measurements are available as well as for the presence of delay, through a well defined piece-wise continuous function depending on the sampling instants and on the output (time-varying) delay. Of particular interest, the proposed observer has the same dimension as the system and is of the high gain variety in the case where the magnitude of the output (time-varying) delay is relatively small. The arbitrarily long delays are handled thanks to a suitable observer structure composed of cascaded subsystems each one of which has the same dimension as the system. More specifically, the cascade observer is first designed in the constant long delay case before being extended to the time-varying long delay case using a suitable procedure. The convergence analysis is performed thanks to a comprehensive Lyapunov approach under a well-defined condition on the maximum value of the sampling partition diameter. The effectiveness of the proposed observer is emphasized through illustrative simulation results.

On exponential stability of switched homogeneous positive systems of degree one

In this paper, we investigate the stability problem of switched homogeneous positive systems of degree one. We first show that the positiveness of the considered system is guaranteed when each switched subsystem is cooperative. Then, an integral excitation condition is formulated to ensure the exponential stability of the switched homogeneous positive system of degree one. In particular, the proposed condition allows that some or even all switched subsystems are only Lyapunov stable rather than asymptotically stable. In the second part of this paper, we further consider the cases of sub-homogeneous systems, time-varying delay systems and discrete-time systems. In the sub-homogeneous case, we first show that the previous integral excitation condition is also sufficient such that the exponential stability is achieved. We also derive an exponential stability result by relaxing the cooperative and integral excitation conditions. In the time-varying delay case, a delay-independent exponential stability result is shown under the extended integral excitation condition. Finally, in the discrete-time case, based on the fact that each switched subsystem is order-preserving instead of cooperative, the exponential stability of the considered system is shown under a weak excitation condition.

Consensus Based Control Algorithm for Nonlinear Vehicle Platoons in the Presence of Time Delay

The platoon control problem for nonlinear vehicles in the presence of time delay is investigated in this paper, where both constant time delay and time-varying delay cases are considered. A linearized third-order vehicle dynamic model is firstly derived by deploying the exact feedback linearization technique and the vehicle platoon control problem is converted into a consensus-seeking problem. Then, a consensus based vehicle platoon control algorithm with time delay is proposed, which drives vehicles to form an equally spaced platoon with the same velocity. By deploying the Lyapunov-Razumikhin theorem, the upper bound of time delay for vehicle platoon with constant time delay is derived and the sufficient conditions that guarantee the stability of the vehicle platoon are obtained. Meanwhile, the sufficient conditions that ensure the stability of vehicle platoon with time-varying delay are acquired via the Lyapunov-Krasovskii theorem. Numerical demonstrations verify the feasibility and correctness of the theoretical results.

Leader-Follower Consensus of Second-Order Multiagent Systems with Absent Velocity Measurement and Time Delay

The leader-follower consensus problem of second-order multiagent systems with both absent velocity measurement and time delay is considered. First of all, the consensus protocol is designed by introducing an auxiliary system to compensate for the unavailability of the velocity information. Then, time delay is incorporated into the consensus protocol and two cases with, respectively, constant time delay and time-varying delay are investigated. For the case of constant time delay, Lyapunov-Razumikhin theorem is deployed to obtain the sufficient conditions that guarantee the stability of the consensus algorithm. For the case of time-varying delay, the sufficient conditions are also derived by resorting to the Lyapunov-Razumkhin theorem and linear matrix inequalities (LMIs). Various numerical simulations demonstrate the correctness of the theoretical results.

Stability of discrete-time positive switched linear systems with stable and marginally stable subsystems

In this paper we investigate the stability of discrete-time positive switched linear systems. The highlight of this work is that each subsystem is only assumed to be stable or marginally stable. Some sufficient conditions, imposed on the subsystem matrices and switching signals, are established to guarantee exponential stability of the considered positive switched linear systems. An extension to the case of time-varying and unbounded delay is also given. Compared with the continuous-time counterparts in the literature, our discrete-time case is much more complicated, involving the transitive connectivity between the subsystems specified by the switching signals.

New Stability Criteria of Delayed Load Frequency Control Systems via Infinite-Series-Based Inequality

A new approach is proposed for the stability problem of delayed load frequency control (LFC) scheme with fixed and time-varying delay cases included in the current paper. New stability criteria with delay dependence in terms of linear matrix inequalities for LFC systems are derived by a novel augmented Lyapunov–Krasovski (L–K) functional. Our proof deployment for system stability of power grids employs the further improved integral inequality in the form of infinite series, which turns out to be less conservative than Wirtinger's inequality that encompasses Jensen inequality. Simulation case studies are carried out to show the effectiveness and superiority of the presented delay-dependent PI-type LFC design scheme.