Delay-dependent Conditions Research Articles

Recovery control of autonomous underwater vehicles based on modified delay-product-type functional

This paper focuses on the recovery process of autonomous underwater vehicles, emphasizing a hierarchical framework in which autonomous underwater vehicles are categorized into a mothership and sub-vessels. In the recovery phase, following the completion of an underwater mission, sub-vessels navigate towards a location designated by the mothership. The crux of the recovery hinges on the design of the controller for adapting communication delays induced by environmental in underwater communication transmissions. The mothership and sub-vessels constitute a collaborative multi-autonomous underwater vehicles network equipped with these controllers, making them operate through the synchronized adjustment of their states represented in error terms. A delay-dependent controller condition criterion is proposed based on the modified delay-product-type Lyapunov-Krasovskii functional. The controller with the gain obtained from the criterion manages the system effectively and ensures successful recovery. The effectiveness of the proposed approach is demonstrated through a case study involving a network comprising one leading and four following autonomous underwater vehicles.

Acute caffeine administration impaired spatial working memory in habitual coffee/tea drinkers: A randomized, placebo-controlled, double-blind study

BackgroundAlthough coffee consumption is widespread worldwide, a recent study showed that acute intake of caffeine negatively affects working memory (WM) performance on n-back tasks among habitual caffeine consumers. However, there is a scarcity of double-blind, placebo-controlled studies that assess the spatial WM (SWM) effects of caffeine using spatial span tasks. Therefore, the present study aimed examine the effects of acute caffeine administration (200 mg, PO) on SWM and verbal WM (VWM) among habitual caffeine consumers. MethodsThe effects of caffeine on working memory (WM) was evaluated through the administration of backward digit span and spatial span tasks under a delay-dependent condition (0, 4, 8, and 6 s) in a randomized, double-blind, placebo-controlled study involving 18 healthy participants. This data is derived from our previous published study. The total scores obtained and the maximum scores achieved were the primary outcome variables of the study. ResultsCaffeine had a significant impact on SWM (maximum obtained, p = 0.013; for total scored, p = 0.007) in a delay-independent manner. However, there were no significant main effects of caffeine on VWM (p = 0.82 for maximum obtained, p = 0.56 for total scored). ConclusionOverall, the present findings contradict the commonly held belief that caffeine improves cognitive performance and suggest that acute administration of caffeine may impair SWM in habitual coffee/tea drinkers. Clinical Trial Registration NumberCT-2018-CTN-02561 (Therapeutic Goods Administration Clinical Trial Registry) and ACTRN12618001292268 (The Australian New Zealand Clinical Trials Registry)

Switched sampled-data-based membership function-dependent [formula omitted] control for PMSG-based WTS with actuator failures

This paper deals with the problem of sampled-data-based H∞ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi-Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in H∞ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD H∞ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique.

Improved results for T-S fuzzy systems with two additive time-varying delays via an extended binary quadratic function negative-determination lemma

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

Flexible Quadrotor Unmanned Aerial Vehicles: Spatially Distributed Modeling and Delay-Resistant Control

This paper introduces an analytical framework for the derivation of distributed-parameter equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, to facilitate the controller design. A delay-resistant low-frequency adaptive controller is employed, which prevents excessive oscillations due to flexible dynamics, compensates uncertainties, and addresses the inherent time delay. In addition to this, a delay-dependent stability condition for the overall system dynamics is obtained including the human operator with reaction time delay, the adaptive controller, and the flexible quadrotor dynamics with input delay. With comparative simulation studies, it is demonstrated that the flexible arm tip oscillations are significantly reduced when the low-frequency delay-resistant closed-loop reference model adaptive controller is used, compared to a closed-loop reference model adaptive controller and a conventional model reference adaptive controller.

Proactive cooperative consensus control for a class of human-in-the-loop multi-agent systems with human time-delays

In this study, we consider a class of human-in-the-loop (HiTL) multi-agent systems that divide agents into two parts: the nonautonomous agents controlled by human operators, and the autonomous agents. First, the human operators’ models are incorporated into the multi-agent system for constructing an HiTL multi-agent system model. Next, the cooperative consensus control problem is explored for the HiTL multi-agent system, and a method is proposed that enables autonomous agents to proactively collaborate with human-controlled agents in order to mitigate the effects of human time-delays. We first obtain the consensus sufficient condition for the HiTL multi-agent system without human time-delays, and then give the method by only designing the autonomous agents’ control gains to guarantee consensus. Subsequently, the delay-dependent consensus sufficient condition for the HiTL multi-agent system with human time-delays is also offered, and the method of controller design is updated for this case. Finally, a simulation experiment was designed, and the simulation results are presented to illustrate the effectiveness of the proposed methods.

Delay-dependent set-invariance for linear difference equations with multiple delays: a polyhedral approach

This paper revisits the set-invariance for linear delay-difference equations and proposes novel delay-dependent notions in contrast with the existing delay-independent constructions available in the literature. The main tool in this endeavour is the model transformation by means of a matrix parametrization, which opens the way to the elaboration of delay-dependent conditions for set invariance. For the class of polyhedral sets, it will be shown how these transformed models enable particularly structured invariance conditions. Aside from the mathematical developments, a discussion of the delay-dependent conditions with respect to the confinement of the state trajectories of the original system will be presented. The relationship will be established by means of constraints involving the initial states for the time-delay systems. The characterization of this set of admissible initial conditions can be analysed in terms of complexity and conservativeness with respect to the classical delay-independent set-invariance. An illustrative example is provided to underline that confinement of state trajectories in a set can be achieved even though this is not invariant according to the classical definition.

Order-Dependent Sampling Control of Uncertain FO Linear System

This paper proposes a sampled-data control problem for the fractional-order system with parameter uncertainties. First, according to the input delay approach, the dynamics of the considered fractional-order system is modeled by a delay system. The main purpose of the problem addressed is to design a sampled-data controller, such that the closed-loop fractional-order system guarantees the asymptotic stability. Then, the Lyapunov-Krasovskii functional is constructed to derive the stable criterion. The new delay-dependent and order-dependent stability conditions are presented in the form of linear matrix inequalities. Eventually, a new sampled-data controller is designed to ensure the stability and stabilization of fractional-order system. Finally, a numerical example is given to illustrate the effectiveness and superiority of the derived criterion.

Global attractivity in tick population models incorporating seasonality and diapausing stages

The goal of this paper is to understand the interplay between seasonality and diapause on the population dynamics of ticks. To analyse this challenge, we study a mathematical model in which the population is divided into two groups: individuals with regular development and individuals undergoing diapause. A key ingredient in the model is that the common birth and death rates depend on time in order to describe the seasonal fluctuations of the environment. From a mathematical point of view, this paper offers a novel methodology to derive criteria of global attraction. In some classical models, we give delay-dependent conditions that cover the best delay-independent criteria of global attraction. We discuss how our approach improves existing results in relevant literature. Moreover, our results are simple and versatile enough to match experimental observations. To illustrate this potential, we analyse our model with parameters coming from real observations. A message of this paper is that seasonality plays a critical role in the population dynamics of ticks.

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

Event-triggered anti-windup strategy for time-delay systems subject to saturating actuators

<p>This paper investigates the anti-windup synthesis problem for linear control systems subject to time-varying state delay and saturating actuators. To alleviate the redundant data transmission, the dynamic event-triggered mechanism is adopted. Moreover, to abate the inherent conservatism, novel delay-dependent sector conditions containing double integral terms are explored. Then, using augmented Lyapunov-Krasovskii functionals and several less conservative inequalities, delay-dependent anti-windup synthesis criteria are obtained in accordance with the feasibility of linear matrix inequalities. Subsequently, the optimization of the initial condition set is addressed. Finally, a simulation example illustrates the availability and technique advantages of the proposed results.</p>

Observer-based fuzzy integral sliding mode control for bilateral teleoperation systems with time-varying delays

This paper aims to examine the stability and tracking performance of a bilateral teleoperation system. The Takagi–Sugeno fuzzy method is utilized, through which the nonlinear master–slave dynamics is converted as a fuzzy-based system. The state observers are designed for the linearized fuzzy teleoperation systems, and the corresponding estimation errors are formulated. Importantly, a novel observer-based fuzzy integral sliding mode control is developed by deliberately introducing the delay term into the sliding surfaces. As such, advanced delay-product type of Lyapunov–Krasovskii functionals are constructed for the augmented state vectors, in order to acquire the additional delay information. In addition, the Wirtinger-based integral inequality along with an extended reciprocally convex matrix inequality is applied to the Lyapunov derivatives to establish the delay-dependent stability conditions. Numerical results are provided to demonstrate efficacy of the developed control mechanism.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Hopf Bifurcation Control of a Fractional-Order Delayed Turbidostat Model via a Novel Extended Hybrid Controller

Building delayed dynamical models to describe the inherent laws of different chemical matters has become a hot theme in recent years. In this current study, we set up a new fractional-order delayed turbidostat model. By using laplace transform, we obtain the characteristic equation of established fractional-order delayed turbidostat model. By selecting the delay as bifurcation parameter and exploring the roots of the corresponding characteristic equation of the involved fractional-order delayed turbidostat model, a novel delay-dependent condition on stability and Hopf bifurcation is acquired. Taking advantage of a novel extended hybrid controller, the stability region and the time of Hopf bifurcation of the established fractional-order delayed turbidostat model are successfully controlled. The role of delay in stabilizing system and controlling Hopf bifurcation is revealed. Matlab experiments are carried out to check the rationality of the acquired key outcomes in this article. The acquired outcomes of this study are completely new and own great theoretical value in dominating concentrations of various chemical matters.

Novel stability conditions for some generalization of Nicholson's blowflies model with stochastic perturbations

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones. doi: 10.1017/S1446181123000147

Enhanced Exponential Stability Analysis for Switched Linear Time-Varying Delay Systems Under Admissible Edge-Dependent Average Dwell-Time Strategy

This article focuses on the exponential stability analysis for the switched linear systems with time-varying delay. By constructing a new augmented multiple Lyapunov–Krasovskii functional, containing time-varying delay information, coupling of current and delayed states, state integral, and state derivative terms the feasibility of the stability condition is considerably enhanced. Besides, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> -order canonical Bessel–Legendre integral inequality and the convex function property are utilized to give more relaxed criteria. On the other hand, for the first time, more flexible switching is employed with an admissible edge-dependent average dwell-time strategy for the switched time-varying delay systems (STDSs). Novel improved delay-dependent stability conditions are expressed by two theorems in the form of linear matrix inequalities which can be used to guarantee the exponential stability of the STDSs in the different delay conditions. Finally, significant improvements over the state-of-the-art in terms of delay upper bound, exponential decay rate, and dwell time are presented by simulating two numerical examples and one practical example including streams water quality preserving.

Caputo−Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays

Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of ∫τωp˙T(s)Sp˙(s)ds often appears in the derivative of Lyapunov−Krasovskii functional, and how to scale down this term to obtain less conservative condition is a key problem. Similarly, the integral term of ∫τω(Dsα0Cp(s))TS0CDsαp(s)ds with fractional derivative may also be encountered in the analysis of dynamical behaviors for fractional-order systems. In view of this, the paper intends to construct several novel fractional Wirtinger integral inequalities under the sense of Caputo derivative, and to investigate the stability of fractional-order systems with mixed time-varying delays based on the constructed Caputo−Wirtinger integral inequalities. Meanwhile, in order to analyze the stability for our concerned models by the new inequalities, two new theorems of generalized fractional-order Lyapunov direct method are given. Finally, a numerical example is designed to validate the correctness and practicability of the obtained results.

Exploring the finite-time dissipativity of Markovian jump delayed neural networks

In this paper, we study the finite-time dissipativity analysis of Markovian jump-delayed neural networks (MJDNNs). The goal is to establish less conservative results for extended dissipativity conditions for delayed MJDNNs. To achieve this, an appropriate Lyapunov-Krasovskii functional (LKF) with novel inequality like composite slack-matrix-based integral inequality (CSMBII). Next, the CSMBII and other sufficient conditions are employed to estimate the derivative of the constructed LKF. Using these techniques, a delay-dependent finite-time dissipativity condition is derived in terms of linear matrix inequalities (LMIs). These LMIs are used to formulate the finite dissipativity condition for the delayed MJNNs. The utility of the suggested approach is then confirmed by a number of interesting numerical examples, one of which has been confirmed by a real-world application of the benchmark problem that is associated with the designed MJDNNs. The illustrative simulation results conclusively demonstrate the superior performance and success of the developed CSMBII technique in this proposal, surpassing the limitations of existing techniques.

Global rational stabilization of a class of nonlinear time-delay systems

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.

Improved delay-dependent stability conditions for discrete-time neural networks with time-varying delays

Improved delay-dependent stability conditions for discrete-time neural networks with time-varying delays