Integral Inequality Technique Research Articles

Containment control for non-linear fractional-order multi-agent systems via refined sample data controller

Abstract This manuscript concentrates on the problem of designing a sampled data controller (SDC) for the consensus of a fractional-order multi-agent system (FOMAS) with Lipschitz non-linearity via an algebraic approach. The solution of the FOMAS is represented by using the Laplace transform approach. An upper bound of the sampling period is determined through various integral inequality techniques. Distinguished from the existing works, the estimate for an upper bound is more accurate which involves the Lipschitz constant of the non-linear function. Finally, numerical examples are given to validate the correctness of results. Furthermore, the comparison results are presented to show the proposed method determines a better upper bound of the sampling period.

Resilient sampled-data control for fractional-order PMVG-based WTS with actuator saturation and probabilistic faults using fuzzy Lyapunov function method

The goal of this study is to present a new fuzzy Lyapunov function-based resilient sampled-data control method for a fractional-order permanent magnet vernier generator (PMVG)-based wind turbine system (WTS) that addresses actuator saturation and probabilistic faults. To achieve this, we first model the dynamical fractional model of the PMVG-based WTS as a T-S fuzzy model. Next, we introduce a fuzzy Lyapunov function within a unified framework that incorporates actuator saturation, probabilistic faults, and uncertainty information from control gain matrices. We then present an actuator fault model that represents actuator faults as stochastic variables with a specific probability distribution. Subsequently, we formulate a robust asymptotic stability criterion for closed-loop systems using linear matrix inequality (LMI), which integrates the fuzzy Lyapunov function and membership function information with fractional integral inequality techniques based on sampling time. We also propose an LMI approach to identify the domain of attraction that meets the necessary actuator saturation criteria. Finally, we apply the proposed method to a PMVG-based WTS, demonstrating its superiority and practical applicability through a comparison with existing methods using a numerical example of a nonlinear truck trailer system.

Finite-time H∞ synchronization of semi-Markov jump neural networks with two delay components with stochastic sampled-data control

This article investigates the finite-time H∞ synchronization for semi-Markov jump neural networks with two delay components based on stochastic sampled data control. Additionally, the parametric uncertainties are randomly varying which follows the Bernoulli distributed sequences. In the stochastic sampled data control, the sampling interval ′m′ is supposed to be two different values in the time-varying component with given probability conditions. By constructing triple and quadruple integral term in the Lyapunov-Krasovskii functional (LKF) a new integral inequality technique is addressed to derive the main results. Dissimilar from previous literature, involving the new integral inequality, a delay dependent finite-time H∞ synchronization requirements are acquired with regard to linear matrix inequalities (LMIs). In the end, the effectiveness of the considered stochastic sampled data control finite time synchronization scheme is highlighted by numerical examples.

Takagi-Sugeno fuzzy sampled-data observer design for nonlinear permanent magnet synchronous generator-based wind turbine systems using auxiliary function-based integral inequality technique

This study focuses on designing the fuzzy sampled-data observer (FSDO) scheme for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS). The primary objective of this problem is to solve an unmeasurable state problem under the mismatched premise variables conditions among system, observer, and controller, respectively. To do this, firstly, the proposed wind turbine model is described in a Takagi-Sugeno fuzzy model due to the complex nonlinearities in PMSG-based WTS. Next, based on the measured output signals and sampled estimated states, the FSDO is designed to understand some unmeasurable state variables of the studied system. Then, a novel auxiliary function-based integral inequality (AFBII) is presented to approximate the integral quadratic terms related to sampling information. Thanks to the proposed AFBII technique and the introduction of slack variables, several new and less conservative stability requirements are derived in the formulations of linear matrix inequalities (LMIs) using the looped Lyapunov function. Finally, the simulation studies for the considered wind turbine model are validated numerically, and then some comparative results are provided to show the superiority and applicability of the theoretical observations.

Exponential stability of non-instantaneous impulsive second-order fractional neutral stochastic differential equations with state-dependent delay

The aim of this manuscript mainly concerned with a new class of exponential stability for non-instantaneous impulsive second-order fractional neutral stochastic differential equations (NIIFNSDEs) with state-dependent delay driven by Poisson jump in a separable Hilbert spaces. Firstly, a more appropriate concept of mild solution is introduced. Secondly, sufficient conditions are derived for the existence of mild solution by means stochastic analysis, fractional calculus approach and Mönch fixed point theorem with appropriate hypotheses on non-linear continuous functions combined with solution operator. Finally, stability results are derived based on the pth moment exponential stable with the help of new impulsive integral inequality techniques. In addition, an example is provided to validate the theoretical results. This manuscript is the unique combination of the new theoretical investigation which is simulated numerically. Our work extends the works of Arthi et al. (2014), Das et al. (2016), Huang et al. (2018), Pandey et al. (2014), Wang et al. (2018), Yan and Jia (2016).

Cooperative Control and Performance Evaluation of a Linear MIMO Parabolic Spatiotemporal Dynamic System on Directed and Switching Topologies.

The current work concerns on cooperative control of exponential stabilization and control performance improvement in the spatial domain for a linear spatiotemporal dynamic system associated with multiple control actuators and multiple collaborative measurement sensors. By assuming that the system dynamics is modeled by a MIMO parabolic partial differential equation (PPDE) and each sensor can share measurement information with its topological neighbors in directed and switching topological networks, a cooperative control protocol is proposed to achieve the control aim of this article. With the help of a combination of multiagent consensus theory, Lyapunov's method, and integral inequality technique, sufficient conditions are presented for the closed-loop exponential stability of the PPDE in the norm |·|2 . Moreover, some performance indexes are defined to evaluate the closed-loop control performance improvement in the spatial domain. Extensive simulation results are finally presented for a simple numerical example and a practical heat treatment process to verify the effectiveness and performance improvement capability of the proposed cooperative control protocol.

Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations

In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend the range of the neutral coefficient. Therefore, our results generalize to some of the results presented in the literature. Furthermore, several examples are provided to illustrate our conclusions.

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

SummaryThe concerns of this article is to investigate the fixed time function combination synchronization (FCS) among three different chaotic systems with disturbances. First, a new stability theorem is presented by virtue of the integral inequality technique and a more accurate upper estimation of the convergence time is given. Next, the fixed time FCS problem is considered for the perturbed chaotic systems in which the scaling functions are generated by the bounded dynamical systems. Besides, the synchronization time is related to the control parameters rather than the initial values. The time upper bound can be calculated out by the simple formula, which is the function of control parameters. Finally, a simulation example is provided to illustrate the correctness of the derived criteria.

Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique

Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique

Fuzzy adaptive event-triggered synchronization control mechanism for T–S fuzzy RDNNs under deception attacks

In this paper, a fuzzy-dependent adaptive event-triggered mechanism (FAETM) for synchronizing Takagi–Sugeno (T–S) fuzzy reaction–diffusion neural networks (RDNNs) is developed while considering deception attacks. Firstly, a general neural network model considering both fuzzy logic rules and reaction–diffusion terms is established. Secondly, a FAETM based on an aperiodic sampling period is presented under deception attacks to alleviate the communication burden, wherein the adaptive threshold function is dependent on membership functions. Moreover, a membership-function-dependent asymmetric Lyapunov functional (LF) is constructed, and some positive-definite and symmetric constraints of matrices are removed as a result. Based on the LF method and integral inequality techniques, the H∞ synchronization criteria for the T–S fuzzy RDNNs are presented by linear matrix inequalities (LMIs). Finally, one simulation example is exploited to demonstrate the feasibility and validity of the established method, and the outcome is applied to image secure communication.

Dissipativity of Stochastic Competitive Neural Networks with Multiple Time Delays

The (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative of stochastic competitive neural networks (SCNNs) with leakage delays and discrete delay is studied. Firstly, Lyapunov–Krasovskii functional is constructed, which studies the relationship between various types of time delays. Secondly, by using integral inequality technique, the linear matrix inequality (LMI) criterion of (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative in the mean square sense of SCNNs is obtained. Furthermore, the obtained LMI criterion is extended to the passivity in the mean square sense, stability in the mean square sense, (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative and passivity. Finally, the effectiveness of the obtained results are verified by numerical simulation.

Delay-independent control for synchronization of memristor-based BAM neural networks with parameter perturbation and strong mismatch via finite-time technology

This paper mainly studies the synchronization problem of memristor-based bidirectional associative memory neural networks (MBAMNNs) via finite-time technology. Different from the existing neural network dynamic models, the given model in this paper is focused on the impact of parameter perturbation and strong mismatch, where strong mismatch includes parameter mismatch and time-varying delay mismatch. These characteristics can make the model be closer to the actual situation. A delay-independent feedback control scheme, which can stabilize the error system within finite-time regardless of whether the past state is known or not, is designed. It is worth noting that the constant is replaced by a function with the exponential term in the delay-independent controller, which can save the control cost to a certain extent. Based on the integral inequality technique, some sufficient conditions for MBAMNNs to converge to the equilibrium point within finite-time are provided. The validity and correctness of the theoretical results are finally confirmed by numerical simulation.

Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays

<abstract> <p>This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.</p> </abstract>

Synchronization sampled-data control of uncertain neural networks under an asymmetric Lyapunov–Krasovskii functional method

This paper investigates the synchronization control of neural networks (NNs) considering parameter uncertainties by utilizing an improved asymmetric Lyapunov–Krasovskii functional (ALKF) method. Firstly, an uncertain NNs model with discrete and distributed delays is developed. To synchronize the master–slave system, a memory sampled-data controller is designed. Secondly, an improved ALKF is constructed, in which the positive-definite and symmetric restrictions of matrices are relaxed. Furthermore, improved synchronization criteria are established by linear matrix inequalities (LMIs), which are based on the ALKF method and the integral inequality technique. Finally, two simulation examples are conducted to demonstrate the feasibility and superiority of the established stability conditions in reaching a maximum sampling period.

Fault estimation for nonlinear parameter-varying time-delayed systems

A fault estimation method for a class of nonlinear parameter-varying systems subject to time-varying delay and unmeasured nonlinearities is presented. The unmeasured time-varying parameters are effectively handled using a sector-based condition approach. A gain-scheduling intermediate estimator is proposed to simultaneously estimate the system state and the unknown faults. Design conditions are derived based on Lyapunov–Krasovskii functional and integral inequality techniques. These conditions, expressed as linear matrix inequalities, ensure that the estimation error dynamics are input-to-state stable with respect to the time-derivative of the faults. Moreover, it is demonstrated that for the case of piecewise constant faults, the estimation error dynamics are exponentially stable. As a corollary result, conditions are also presented to design gain-scheduling intermediate estimators for nonlinear parameter-varying systems without time-varying delays. Three physically motivated examples are provided to demonstrate the effectiveness and practical interests of the proposed nonlinear estimation method.

A delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network models with distributed coupling delays

This paper studies the issue of delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network (MJCDN) models with distributed coupling delays. The state feedback control scheme is designed for the synchronization of the MJCDN closed-loop error model. By constraining the appropriate Lyapunov functional along with the properties of the Kronecker product and using integral inequality techniques,several new delay dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs), which ensure that the dissipativity and passivity performance of the considered MJCDN model. The results of this analysis are verified using the MATLAB LMI control toolbox. Illustrative examples are provided to demonstrate the feasibility of the results

Nonfragile power and frequency control in islanded microgrids under abnormal asynchronous stochastic cyber attacks

In this paper, we focus on the real power sharing and frequency regulation of distributed generators in islanded microgrids with abnormal asynchronous stochastic cyber attacks, which is of great significance to the information security and stable operation of microgrids. Firstly, considering the possible cyber attacks in the communication network, a distributed non-fragile controller with coupled memory delay is proposed according to the nonperiodic sampled-data control. Then, the construction of delay-dependent two-sided looped-functional makes the Lyapunov–Krasovskii functional contain more delay and sampling information and relaxes constraints on free matrices. In addition, based on the enhanced integral inequality technique and the linear convex combination method, a sampling-based consensus protocol is presented to solve the issues of real power sharing and frequency regulation in the islanded microgrids. Finally, to verify the effectiveness and feasibility of the designed control strategy, a modified IEEE 34-bus test system is used for the experiment.

Finite-Time Fuzzy Boundary Control for 2-D Spatial Nonlinear Parabolic PDE Systems

Seldom existing studies directly focus on the control issues of two-dimensional (2-D) spatial PDE systems, although they have strong application backgrounds in production and life. Therefore, this article investigates the finite-time control problem of an 2-D spatial nonlinear parabolic PDE system via T–S fuzzy boundary control scheme. First, the overall fuzzy system model is constructed using T–S fuzzy rules to approximate the original nonlinear system. Second, based on the planar distributed measurement, boundary collocated measurement, and linear measurement methods, three novel kinds of fuzzy boundary controllers are designed. Then, by employing the variable substitution and integral inequality techniques, three criteria that ensure the finite-time boundness of the considered system are obtained. Finally, simulations of main results are provided to verify the effectiveness and practicability of the proposed measurement and control schemes.

Finite-Time Synchronization of Quantized Markovian-Jump Time-Varying Delayed Neural Networks via an Event-Triggered Control Scheme under Actuator Saturation

In this paper, we present a finite-time synchronization (FTS) for quantized Markovian-jump time-varying delayed neural networks (QMJTDNNs) via event-triggered control. The QMJTDNNs take into account the effects of quantization on the system dynamics and utilize a combination of FTS and event-triggered communication to mitigate the effects of communication delays, quantization error, and efficient synchronization. We analyze the FTS and convergence properties of the proposed method and provide simulation results to demonstrate its effectiveness in synchronizing a network of QMJTDNNs. We introduce a new method to achieve the FTS of a system that has input constraints. The method involves the development of the Lyapunov–Krasovskii functional approach (LKF), novel integral inequality techniques, and some sufficient conditions, all of which are expressed as linear matrix inequalities (LMIs). Furthermore, the study presents the design of an event-triggered controller gain for a larger sampling interval. The effectiveness of the proposed method is demonstrated through numerical examples.

Internet of health things encryption via master-slave synchronization for stochastic quaternion-valued neural networks

This paper investigates the problem of master-slave synchronization of stochastic quaternion-valued neural networks (SQVNNs) with mixed time-varying delays. A linear feedback controller is developed to explore the global synchronization of the proposed system by utilizing the complete information of the time-delay state. Sufficient conditions for synchronization of the proposed model are derived by constructing appropriate Lyapunov–Krasovskii functional by applying the master-slave synchronization method of master-slave and some integral inequality techniques. Finally, a corresponding numerical simulation is presented to demonstrate the accuracy of the theoretical results. This paper introduces a unique and efficient image encryption algorithm based on SQVNNs. This technique utilizes the solution set of SQVNNs to generate the high-level randomness secret keys to encrypt the source image. Finally, we conclude that the algorithm yields a source image cipher with excellent diffusion and confusion properties. A few test clinical images are utilized to show the validity of the proposed method. Several performance analyses show that the proposed algorithm for image encryption gives an efficient and secure way to deal with the Internet of Health Things (IoHT).