Interval Time-varying Delay Research Articles

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

<abstract><p>This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.</p></abstract>

New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

<abstract><p>For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.</p></abstract>

Formula omitted] control for singular systems with interval time-varying delays via dynamic feedback controller

The issue of dynamic feedback H∞ control in this paper is carefully revisited for singular systems with interval time-varying delays. A Lyapunov-Krasovskii functional, made up of state decomposition components and relatively few decision variables, is proposed. Further, a delay-dependent admissible criterion (conforming to non–impulsiveness, regularity, and stability) with a given H∞ performance index for the unforced nominal singular systems is founded by some linear matrix inequalities. Subsequently, a dynamic feedback controller for the closed–loop system is designed and the corresponding admissibility conditions are obtained. By means of a state decomposition recombination method, the desired dynamic feedback controller parameters are clearly determined by solving each decomposition component of the dynamic feedback controller. Interestingly, our results can enhance the previous results and the method proposed has greater flexibility. By numerical examples, some comparisons are shown to reveal the superiority and feasibility of our method.

Two novel stability criteria for linear systems with interval time-varying delays

This paper analyses the stability problem of linear systems with interval time-varying delay. In regard to the delay, it has the lower and upper bounds and its derivative is unknown or itself is not differentiable. First of all, it is the first time that the delay-related triple integral terms are used to construct the augmented Lyapunov–Krasovskii functional (LKF) and the delay-related integral quadratic terms are estimated by the third-order free-matrix-based integral inequalities (TFIIs). Then, based on the same LKF and same TFIIs and by introducing two sets of state vectors, the derivative of the LKF is presented as the quadratic and quintic polynomials about the delay respectively. Next, for the quadratic and quintic polynomials, new negative definite conditions (NDCs) are provided to form the linear matrix inequality (LMI) conditions. Finally, the advantages of these two criteria are checked through some classical numerical examples.

Robust H∞ Controller Design of Switched Delay Systems with Linear Fractional Perturbations by Synchronous Switching of Rule and Sampling Input

In this paper, we propose synchronous switching of rule and input to achieve H∞ performance for an uncertain switched delay system with linear fractional perturbations. Our developed simple scheme utilizes the linear matrix inequality optimization problem to provide a feasible solution for the proposed results; if the optimization problem was feasible, our proposed robust H∞ control could be designed. The feasibility of the optimization problem could be solved using the LMI toolbox of Matlab. In this paper, robust control with sampling is proposed to stabilize uncertain switching with interval time-varying delay and achieve H∞ performance. Interval time-varying delay and sampling were considered instead of constant delay and pointwise sampling. A full-matrix formulation approach is presented to improve the conservativeness of our proposed results. Some numerical examples are demonstrated to show our main contributions.

Exponential H∞ stabilization of uncertain neural networks with time-varying delay and external disturbance via periodically intermittent control

This paper is concerned with the exponential [Formula: see text] stabilization for a class of uncertain neural networks with interval time-varying delay and external disturbance via periodically intermittent control. By constructing a novel Lyapunov–Krasovskii functional (LKF) and applying some inequality techniques, delay-dependent sufficient conditions are derived to guarantee the exponential [Formula: see text] stabilization of the considered closed-loop system. These conditions are given in the form of linear matrix inequalities (LMIs). The intermittent state-feedback controller can reduce the effect of external disturbance to a prescribed attenuation level [Formula: see text]. Furthermore, the desired controller gain matrix can be obtained by solving the obtained LMIs. Finally, numerical simulations are given to show the effectiveness and the benefits of the proposed method.

A relaxed binary quadratic function negative-determination lemma and its application to neutral systems with interval time-varying delays and nonlinear disturbances

This paper considers the stability problem of neutral systems with interval time-varying delays and nonlinear disturbances. Firstly, an augmented vector containing two double integral terms is introduced into the Lyapunov-Krasovskii functional (LKF). In this case, a binary quadratic function with discrete and neutral delay arises in the time derivative. To gain the negativity condition of such function, by taking full advantage of the idea of partial differential of the binary quadratic function and Taylor's formula, a relaxed binary quadratic function negative-determination lemma with two adjustable parameters is proposed, which contains the existing lemmas as its special cases and shows the great potential of reducing conservatism for the case where the tangent slope at the endpoint is far from zero. Then, based on the improved lemma, more relaxing stability criteria have been obtained via an augmented LKF. Finally, two classic numerical examples are given to attest the effectiveness and strengths of the obtained stability criteria.

Finite-time H∞ synchronization control for coronary artery chaos system with input and state time-varying delays.

This is the first time for studying the issue of finite-time H∞ synchronization control for the coronary artery chaos system (CACS) with input and state time-varying delays. Feedback control is planned for finite-time of synchronization CACS. By constructing the Lyapunov-Krasovskii functional (LKF) is derived for finite-time stability criteria of CACS with interval and continuous differential time-varying delays. We use Wirtinger-based integral inequality to evaluate the upper bound of the time derivative of the LKF. We apply the single integral form and the double integral form of the integral inequality, according to Wirtinger-based integral inequality, to ensure that the feedback controller for synchronization has good performance with disturbance and time-varying delay. The new sufficient finite-time stability conditions have appeared in the form of linear matrix inequalities (LMIs). Numerical checks can be performed using the LMI toolbox in MATLAB. A numerical example is presented to demonstrate the success of the proposed methods. This resultant is less conservative than the resultants available in the previous works.

Novel robust stability analysis method for uncertain systems with interval time-varying delay

Novel robust stability analysis method for uncertain systems with interval time-varying delay

Robust Mixed Performance Control of Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay by Sampled-Data Input

In this paper, a sampled-data parallel distributed compensator (PDC) is proposed to guarantee mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}/H_{\infty }$ </tex-math></inline-formula> performance of uncertain T-S fuzzy systems with interval time-varying delay and linear fractional perturbations. A full matrix formulation approach is developed to present our main results in LMI conditions. To achieve better results, new inequality and Lyapunov-Krasovskii functional are developed to improve the conservativeness of the proposed results. Finally, some numerical examples are illustrated to show the use of our main results. In this paper, interval time-varying delay and interval sampling are considered instead of constant delay and periodic sampling in published literatures.

Investigation of convergence behavior on fuzzy system

This paper studies the convergence behavior of a type of T-S fuzzy system with interval time-varying delay and nonlinear perturbations. A delay partitioning method is used to construct a modified Lyapunov Krasovskii functional(LKF) including triple-integral terms and augmented factors, which is introduced from these equidistant subintervals. In addition, the Free-Matrix-Based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. Eventually, much less conservative results are presented. Numerical analyses are conducted to demonstrate the evaluation of this proposed research development.

Adaptive LFC Incorporating Modified Virtual Rotor to Regulate Frequency and Tie-Line Power Flow in Multi-Area Microgrids

This research investigates a new coordination strategy for both isolated single-area and interconnected multi-area microgrids (MGs) using a modified virtual rotor-based derivative technique supported with Jaya optimizer based on balloon effect modulation (BE). Accordingly, the main concept of BE is to assist the classic Jaya to be more sensitive and trackable in the event of disturbances, as well as to provide optimum integral gain value on the secondary frequency controller adaptively for both suggested MGs. The proposed modified virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs considering full participation of the inverter-based energy storage systems. The proposed virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs to emulate the reduction in system inertia and the enhanced damping properties. Several nonlinearities were proposed in this work such as a dead band of governor, generation rate constraints, and communication time-delay are considered within the dynamic model of the suggested MGs. In addition, the proposed design of multi-area MGs takes the interval time-varying communication delays into account for stability conditions. In this study, A comparative study using unimodal (i.e., Sphere) and multimodal (i.e., Rastrigin) benchmark test functions are conducted to validate the proposed direct adaptive Jaya-based BE. Furthermore, Wilcoxon’s rank-signed non-parametric statistical test using a pairwise comparison was performed at a 5 % risk level to judge whether the proposed algorithm output varies from those of the other algorithms in a statistically significant manner. Thence, the superiority and effectiveness of the proposed method have also been verified against a variety of other metaheuristics optimization techniques, including classic electro-search, particle swarm, multi-objective seagull, and Jaya optimizers. In addition, an operative performance is assessed against the conventional integral controller, coefficient diagram method, and classic Jaya with/without virtual inertia. The final findings emphasize the superiority of the proposed direct adaptive Jaya-based BE supported by a modified virtual rotor and state better performance and stability compared to existing controllers.

Modified function projective synchronization of master-slave neural networks with mixed interval time-varying delays via intermittent feedback control

&lt;abstract&gt;&lt;p&gt;The modified function projective synchronization problem for master-slave neural networks with mixed interval time-varying delays is presented using periodically intermittent feedback control. The interval distributed time-varying delay including the lower and upper bound is comprehensively established, which developed from the previous work. The following techniques are utilize to analyze the appropriate criteria for the modified function projective synchronization problem for master-slave neural networks with mixed interval time-varying delays such as the construction of appropriate Lyapunov-Krasovskii functionals merged with Newton-Leibniz formulation method, the intermittent feedback control technique, the reciprocally convex technique's lower bound lemma, Jensen's inequality, and the piecewise analytic method. The sufficient criteria for the modified function projective synchronization of the error system between the master and slave neural networks with intermittent feedback control are first established in terms of linear matrix inequalities (LMIs). The designed controller ensures that the synchronization of the error systems are proposed via intermittent feedback control. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.&lt;/p&gt;&lt;/abstract&gt;

Improved Extended Dissipativity Results for T-S Fuzzy Generalized Neural Networks With Mixed Interval Time-Varying Delays

The asymptotic stability and extended dissipativity performance of T-S fuzzy generalized neural networks (GNNs) with mixed interval time-varying delays are investigated in this paper. It is noted that this is the first time that extended dissipativity performance in the T-S fuzzy GNNs has been studied. To obtain the improved results, we construct the Lyapunov-Krasovskii functional (LKF), which consists of single, double, triple, and quadruple integral terms containing full information of the delays and a state variable. Moreover, an improved Wirtinger inequality, a new triple integral inequality, and zero equation, along with a convex combination approach, are used to deal with the derivative of the LKF. By using Matlab’s LMI toolbox and the above methods, the new asymptotic stability and extended dissipativity conditions are gained in the form of linear matrix inequalities (LMIs), which include passivity, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}-L_{\infty }$ </tex-math></inline-formula> , <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> , and dissipativity performance. Finally, numerical examples that are less conservative than previous results are presented. Furthermore, we give numerical examples to demonstrate the correctness and efficacy of the proposed method for asymptotic stability and extended dissipativity performance of the T-S fuzzy GNNs, including a particular case of the T-S fuzzy GNNs.

Further results on stabilization for neutral singular Markovian jump systems with mixed interval time-varying delays

This paper focuses on the mean-square exponentially (ME) admissibility and stabilization for neutral singular Markovian jump systems (NSMJSs) with mixed interval time-varying delays. With the aid of state decomposition approach, a state decomposition Lyapunov-Krasovskii functional (LKF) is founded and some mode-dependent conditions are given to guarantee the unforced NSMJSs to be ME admissible. On this basis, a mode-dependent state feedback controller is presented. By solving the decomposition components of state feedback control parameters, the designed state feedback controller is obtained. It should be pointed out that our results complement and improve the results of the existing literatures. By two number-based examples, the advantage and availability of our methods are presented.

Robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay

This paper deals with the problem of delay-range-dependent robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. The uncertainties under consideration are norm-bounded uncertainties and the restriction on the derivative of the discrete and distributed interval time-varying delays is removed, which means that a fast interval time-varying delay is allowed. By applying a novel Lyapunov-Krasovskii functional approach, improved integral inequalities, Leibniz-Newton formula and utilization of zero equation, then a new delay-range-dependent passivity criterion of neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay is established in terms of linear matrix inequalities (LMIs). Furthermore, some less conservative delay-dependent passivity criteria are obtained. Moreover, we derived a robust passivity criterion for uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. Besides, a less conservative delay-dependent robust passivity criterion is obtained. Finally, five numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.

Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays

In this study, the challenges of the controller design of a class of Uncertain Switched Neutral Systems (USNSs) in the presence of discrete, neutral, and time-varying delays are considered by using a robust observer-based control technique. The cases where the uncertainties are normbounded and time-varying are emphasized in this research. The adopted control approach reduces the prescribed level of disturbance input on the controlled output in the closed-loop form and the robust exponential stability of the control system. The challenge of parametric uncertainty in USNSs is solved by designing a robust output observer-based control and applying the Yakubovich lemma. Since the separation principle does not generally hold in this research, the controller and observer cannot be designed separately, sufficient conditions are suggested. These conditions are composed of applying the average dwell time approach and piecewise Lyapunov function technique in terms of linear matrix inequalities, which guarantees robust exponential stability of the observer-based output controller. Finally, two examples are given to determine the effectiveness of the proposed method.

Analysis and Design of Photovoltaic Nonlinear System: A Delta Operator Fuzzy Control Scheme

Aims: The paper is concerned with the problem of robust H∞ output feedback control for photovoltaic nonlinear system. Background: The PV systems are built to transform sun irradiance into electrical power. The dc-dc converters, such as buck type, boost type, and buck-boost type, have been widely implemented in the PV systems. Linear controllers for dc-dc converters are often designed based on mathematical models. To get a desired performance objective, an accurate model is essential. Objective: There has been increasing interest in the scheme of digital controller design for dc-dc converters. However, most of the research efforts are focused on the representation based on the standard forward-shift operator approach, which are of inherently ill-conditioned when datum are taken at high sampling rates. Compared with the forward-shift operator, the delta operator has many virtues which can be applied as a better representation of the underlying physical model under high sampling rates. Despite the delta operator possessing the superior high sample rate performance has been recognized in the past two decades, there exists little literature discussing the analysis and synthesis of photovoltaic nonlinear systems by using delta operator fuzzy control method, which motivates us to make an effort in this topic. Methods: We propose a Fuzzy Dynamic Output Feedback (FDOF) controller, and introduce a novel Lyapunov-Krasovskii Functional (LKF) in delta domain, the framework of robust H∞ output feedback control is investigated. Results: Sufficient conditions are derived for the existence of the desired FDOF controllers in terms of Linear-Matrix Inequalities (LMIs). A numerical example is used to illustrate the design procedure of the present method. Conclusion: This paper has studied the problems of robust H∞ output feedback control for photovoltaic nonlinear system with interval time-varying delay and parametric uncertainties. Based on the formulated fuzzy system and the FDOF controller, we introduced a Lyapunov-Krasovskii function in delta domain, the scheme of FDOF was proposed. Sufficient conditions for the existence of the FDOF controller were derived in terms of LMIs. A numerical example was used to demonstrate the effectiveness of our proposed methods.

Fault-tolerant control for uncertain switched random systems with multiple interval time-varying delays and intermittent faults

Fault-tolerant control for uncertain switched random systems with multiple interval time-varying delays and intermittent faults