Lyapunov-Krasovskii Functionals Research Articles

A memory state-feedback controller via random pocket dropouts for multi-agent systems with external disturbance

This study explores the challenge of achieving consensus in multi-agent systems (MASs) when facing the random packet dropouts and disturbances. It employs memory state-feedback control (MSFC) in the context of undirected graphs and specified leader agents. The analysis focuses on mean square consensus, considering MASs within strongly connected networks or networks with undirected spanning trees. The MSFC approach is developed to ensure asymptotic consensus despite packet dropouts and also to reduce the impact of disturbances. Specifically, the consensus analysis leverages the Lyapunov-Krasovskii functional (LKF) framework, and the necessary conditions for implementing the proposed MSFC are established using linear matrix inequalities (LMIs). The system, augmented with an H ∞ attenuation level is guaranteed to achieve asymptotic mean-square stability according to the provided criteria. In conclusion, two examples are provided to illustrate the effectiveness and practicality of the proposed control mechanism.

A non-singular terminal sliding mode controller for a communication-based hybrid microgrid

The paper proposes a robust and effective networked control for a hybrid based islanded microgrid. Renewable energy sources with energy storage systems are linked in parallel using voltage source inverters to supply the loads in a microgrid. The master-slave control strategy is implemented. CAN and the ZigBee networks are selected to share data, where the master controller transmits the reference signals to the slave controllers in the microgrid via these two networks. As the control loop incorporates a communication network and energy storage systems, the impacts of external disturbances, parametric uncertainties, and time delay executed by the devices introduce challenges in control of voltage and current. Thereby, it is crucial to use a robust and stable control approach. Using the binary iteration algorithm, stability criteria in the form of linear matrix inequalities based on the Lyapunov-Krasovskii function are employed to derive the system's maximum allowable delay boundary. As the reliability of the communication network can be affected, a nonsingular terminal sliding mode controller is employed. The proposed robust control method was implemented in MATLAB/Simulink and the True-time 2.0 simulator and its performance were evaluated under different loads, uncertainties, disturbances, and communication impairments. Simulation results show that the desired performance i.e., maintaining the microgrid's stability with accurate voltage and current control even in unallowable delay limits is met.

A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties

This paper proposes a novel robust tracking control scheme for discrete time linear uncertain Multiple-Input Multiple-Output (MIMO) systems subject to time-varying delay on the states. The considered system is affected by unknown but norm bounded uncertainties on parameters as well as matched disturbances on the states. The designed controller is based upon a proposed novel integral sliding surface and a new switching type of reaching law. Sufficient conditions based on Linear Matrix Inequalities (LMIs) and a suitable Lyapunov–Krasovskii Functional (LKF) are derived in order to guarantee the asymptotic stability of such system. The proposed controller ensures a good tracking performance despite the presence of the time varying delay and the matched/unmatched disturbances. Moreover and thanks to the proposed integral surface, the time reaching phase is eliminated and the chattering phenomenon is significantly reduced. The proposed controller is applied on an Autonomous Underwater Vehicle (AUV) to follow a prescribed desired trajectory. The simulation results illustrate the effectiveness of such controller.

Resilient and event-triggered control of singular Markov jump systems against cyber attacks

This paper is concerned with the H ∞ resilient and event-triggered control of singular Markov jump systems against deception attacks. The deception attacks are modelled as a random bounded signal which is governed by a Bernoulli distributed random variable. The event-triggered scheme is adopted to achieve a trade-off between system performance and network resources. Based on the technique of stochastic Lyapunov–Krasovskii functionals and linear matrix inequalities, efficient criteria are developed such that the closed-loop system is stochastically admissible with a certain H ∞ performance under deception attacks. Then, the co-design of resilient controller gains and event-triggered rules is provided in terms of a group of feasible LMIs. Finally, two examples are employed to verify the validity of our design.

Event‐triggered security control for fuzzy‐model‐based cyber‐physical systems under Denial‐of‐Service attacks and actuator faults

AbstractThis article addresses the issue of event‐triggered security control for nonlinear cyber‐physical systems, characterized by Denial‐of‐Service (DoS) attacks, time‐varying delays, and actuator faults. These complexities are captured using the Takagi–Sugeno fuzzy model. Significantly, this study focuses on DoS attacks targeting the controller‐to‐actuator channel, and subsequently introduces a model for actuator faults that considers the prolonged utilization or degradation of component parts. To optimize communication resource allocation, a model‐independent event‐triggered mechanism is proposed. Utilizing the Lyapunov–Krasovskii function approach, the objective of achieving stochastic stability is transformed into a linear matrix inequalities problem, thus deriving a set of sufficient conditions. The efficiency and validity of the proposed algorithms is demonstrated through simulation results.

Adaptive guaranteed cost control for nonlinear systems with unknown parameters and time delays based on fully actuated system approaches

This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov–Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method.

Stability analysis of linear systems with time-varying delay via some novel techniques

This paper concentrates on the stability analysis of linear systems with a time-varying delay. Firstly, a new Lyapunov–Krasovskii functional (LKF) is given, which involves more time delay cross-terms information. Secondly, an improved reciprocally convex inequality with higher estimation accuracy is derived. Then, on the basis of the constructed LKF and the improved reciprocally convex inequality, some new stability criteria with less conservative are proposed. Finally, the superiority of the obtained stability criteria is explained by two numerical examples.

A sampled-data stabilisation analysis on memristive BAM neural networks for memductance function

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results.

Frequency regulation scheme in power system using an observer-based waiting event-triggered control with random features

Addressed in this paper is the observer-based waiting event-triggered control issue in multi-area load frequency control (LFC) power system subject to random communication delay and data packet dropout. In order to maintain the grid frequency stability of the multi-area LFC power system in an open communication network, an observer-based waiting event-triggered scheme (WETS) is proposed to deal with frequency fluctuation and extend the life of control equipments. Compared with the existing event-triggered mechanism, the proposed WETS has the merits of continuous event-triggered scheme and the periodic sampling event-triggered scheme in the both of theory and application. Then, by well considering the negative factors of data packet dropout and random time delay in data transmission, a stochastic delay-dependent multi-area LFC model is established, which involves the information of observer-based WETS, random communication delay and packet dropout in a unified structure. Further, an improved Lyapunov–Krasovskii functional (LKF) is constructed by dividing the interval of transmitted delay. Based on the constructed Lyapunov functional, Park’s theorem and Jensen’s integral inequality, some less conservative stabilization criteria are obtained. Finally, the validity of the proposed control method is verified via numerical examples.

Quantized fault-tolerant pinning control for finite-time H∞ synchronization of T-S fuzzy discrete Markovian-jump complex networks subject to heterogeneous delays

This paper investigates the finite-time pinning synchronization problem for a class of T-S fuzzy discrete Markovian-jump complex networks (TSFDMCNs) influenced by heterogeneous delays. The evolution of system parameters follows the Markov jump process according to a transition probability matrix with partly unknown elements. Based on the system state output, quantized fault-tolerant pinning controller (QFTPC) is designed to overcome communication limitations and varying actuator fault. Besides, the asynchronous signal generated by the hidden Markov model is employed in controller to make full use of received information. A novel mode-dependent Lyapunov- Krasovskii functional (LKF) is established to guarantee the error system mean-square finite-time bounded with the prescribed performance. In order to reduce conservatism of derived results, an improved Wirtinger-based inequality technique is applied in considering both lower and upper bounds of different delay. Finally, simulation examples illustrate the effectiveness and meliority of the proposed theoretical methods.

Improved Stability Analysis Results of Generalized Neural Networks With Time-Varying Delays.

This article studies the stability problem of generalized neural networks (GNNs) with time-varying delay. The delay has two cases: the first case is that the delay's derivative has only upper bound, the other case has no information of its derivative or itself is not differentiable. For both two cases, we provide novel stability criteria based on novel Lyapunov-Krasovskii functionals (LKFs) and new negative definite conditions (NDCs) of matrix-valued cubic polynomials. In contrast with the existing methods, in this article, the proposed criteria do not need to introduce extra state variables, and the positive-definite constraint on the novel LKF is relaxed. Moreover, based on free-matrix-based inequality (FMBI) and new NDCs, the stability conditions are expressed as linear matrix inequalities (LMIs). Eventually, the merits and efficiency of the proposed criteria are checked through some classical numerical examples.

Aperiodic Sampled-Data-Based Control for T-S Fuzzy Systems: An Improved Fuzzy-Dependent Adaptive Event-Triggered Mechanism

This paper is devoted to designing a novel aperiodic sampled-data-based event-triggered control strategy for Takagi-Sugeno (T-S) fuzzy systems. Firstly, via taking the structural features of fuzzy subsystems and the available information of fuzzy membership functions (FMFs) into consideration, an improved fuzzy-dependent adaptive event-triggered mechanism (FDAETM), which designs different adaptive event-triggered mechanisms for corresponding fuzzy subsystems, is proposed to provide extra design flexibility and further optimize communication efficiency. Then, the two-side looped-functional method (TSLFM) and dynamic partitioning approach are introduced in the construction of the novel Lyapunov-Krasovskii functional (LKF). These two methods contribute to deriving preferable stability criterion and stabilization approach via relaxing the positive definite constraint on LKF and fully utilizing the inner system state during the whole aperiodic sampling interval. Eventually, two simulation examples are introduced to verify the effectiveness of the proposed control strategy and its advantages in lightening communication frequency.

Input–Output Finite-Time Stability for Switched T–S Fuzzy Delayed Systems With a Time-Dependent Lyapunov–Krasovskii Functional Approach

This research concerns the finite-time performance analysis for switched Takagi-Sugeno (T-S) fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input-output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input-output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input-output) finite-time analysis framework.

Distributed Coordination LFC Approach for Interconnected Power Systems Under Detection and Compensation Mechanism Targeting DoS Attacks

A distributed coordination load frequency control (LFC) approach is proposed for interconnected power systems, and a detection and compensation mechanism targeting denial-of-service (DoS) attacks is designed in this work. Firstly, different from traditional LFC, a hybrid-type distributed control strategy is proposed, which takes full advantage of local control information and coordination control information. Then, for discovering DoS attacks timely, a feasible detection algorithm targeting DoS attacks is presented. Furthermore, in order to weaken the harm of cyber-attacks, a triggered-type compensation mechanism for control data is proposed. By constructing appropriate Lyapunov-Krasovskii functionals, a stability criterion with an <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> performance index is developed. At last, the feasibility of detection and compensation mechanism targeting DoS attacks and the effectiveness of proposed control approach are demonstrated by presenting contrastive illustrative examples.

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.

Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay

This work presents a generalized delay-dependent reciprocally convex inequality (GDDRCI) to analyze the stability problem of neural networks (NNs) with time-varying delay. The proposed GDDRCI with its order m in this research improves the estimation accuracy of a reciprocal convex term and encompasses some existing reciprocally convex inequalities as a special case. Consequently, a novel Lyapunov–Krasovskii functional (LKF), which includes a delay-product type m-dependent term and utilizes the correlated cross-information about the states and nonlinear activation function, is formulated. Since the constructed GDDRCI and LKF, the conservatism of the resulting stability conditions of NNs is further decreased. Finally, four numerical examples are presented to demonstrate the importance of the theoretical results.

Almost Surely Exponential Convergence Analysis of Time Delayed Uncertain Cellular Neural Networks Driven by Liu Process via Lyapunov-Krasovskii Functional Approach.

As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibrium states (or fixed points) of time delayed uncertain cellular neural networks driven by the Liu process. By applying the classical Banach's fixed-point theorem, we prove, under certain conditions, that the delayed uncertain cellular neural networks, concerned in this paper, have unique equilibrium states (or fixed points). By carefully designing a certain Lyapunov-Krasovskii functional, we provide a convergence criterion, for state trajectories of our concerned uncertain cellular neural networks, based on our developed Lyapunov-Krasovskii functional. We demonstrate under our proposed convergence criterion that the existing equilibrium states (or fixed points) are exponentially stable almost surely, or equivalently that state trajectories converge exponentially to equilibrium states (or fixed points) almost surely. We also provide an example to illustrate graphically and numerically that our theoretical results are all valid. There seem to be rare results concerning the stability of equilibrium states (or fixed points) of neural networks driven by uncertain processes, and our study in this paper would provide some new research clues in this direction. The conservatism of the main criterion obtained in this paper is reduced by introducing quite general positive definite matrices in our designed Lyapunov-Krasovskii functional.

Observer-Based State Estimation for Recurrent Neural Networks: An Output-Predicting and LPV-Based Approach

An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that individually estimate the state of the neurons at various periods. This new cascade predictor is more useful than the conventional single observer in predicting neural network states when the output delay is arbitrarily large but known. In contrast to examining the stability of error systems solely employing the Lyapunov–Krasovskii functional (LKF), several new global asymptotic stability standards are obtained by combining the application of the Linear Parameter Varying (LPV) approach, LKF and convex principle. Finally, a series of numerical simulations verify the efficacy of the obtained results.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Exponential stability of delay dependent neutral-type descriptor neural networks with uncertain parameters

The idea of delay-dependent states of neutral-type uncertain descriptor neural networks with mixed delays in time-varying sense (i.e. discrete & distributed) and leakage delays is implemented in this study. By building a modern LKF (Lyapunov–Krasovskii functional) and enlisting some analysis techniques, new stability conditions for the designated neural networks are derived in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI toolbox. To do that, the research that is being offered here is more advanced and less constrained than the previous one that has been published in the literature. Two numerical examples with simulations and some novel comparative statements are carried out to demonstrate the benefit and validity of our theoretical conclusions.