Interval Time-varying Delay Research Articles

Finite Time Stability Analysis and Feedback Control for Takagi–Sugeno Fuzzy Time Delay Fractional-Order Systems

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi–Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations.

Stability and stabilization of fractional-order singular interconnected delay systems

An analytical approach based on fractional calculus and singular value theory to finite-time stability and stabilization of fractional-order singular interconnected delay systems is proposed. Particularly, we study fractional singular equations with interval time-varying delays. We first give new sufficient conditions for finite-time stability of such equations. Then, the feedback stabilizing controllers are designed via solving a tractable linear matrix inequality (LMI) and Mittag-Leffler function. Finally, numerical examples with simulations are given to illustrate the feasibility and effectiveness of the proposed results.

Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional

This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality (WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality (LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. Then, simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems.

Analysis of finite-time stability in genetic regulatory networks with interval time-varying delays and leakage delay effects

<p>We primarily examined the effect of leakage delays on finite-time stability problems for genetic regulatory networks with interval time-varying delays. Since leakage delays can occur within the negative feedback components of networks and significantly impact their dynamics, they may potentially cause instability or suboptimal performance. The derived criteria encompass both leakage delays and discrete interval time-varying delays through the construction of a Lyapunov-Krasovskii function. We employed the estimation of various integral inequalities and a reciprocally convex technique. Additionally, these models consider lower bounds on delays, which may be either positive or zero, and allow for the derivatives of delays to be either positive or negative. Consequently, new criteria for genetic regulatory networks with interval time-varying delays under the effect of leakage delays are expressed in the form of linear matrix inequalities. Ultimately, a numerical example is presented to show the effect of leakage delays and to emphasize the significance of our theoretical findings.</p>

Parametric Stability Criteria for Delayed Recurrent Neural Networks via Flexible Delay-Dividing Method.

This article focuses on investigating the stability issue for recurrent neural networks (RNNs) with interval time-varying delays (TVDs) based on a flexible delay-dividing method with parameters, which are related to the delay derivative. First, an interval of delay is separated into parametric subintervals via the linear combination technique. Then, an establishment of Lyapunov-Krasovskii functional (LKF) is connected to the parameters, and a novel linear technology is suggested to dispose of integral terms in the derivatives of the constructed function. Finally, the validity and advantage of the inferred criteria are interpreted by the comparison of representative simulation examples.

Hierarchical stability conditions for linear systems with interval time-varying delay

This paper proposes the hierarchical stability conditions for linear systems with an interval time-varying delay. In the matter of the delay, the upper and lower bounds are restricted, but there is no constraint on its derivative. Firstly, based on the state vectors and multiple integral state vectors involved in the delay-related generalized free-matrix-based integral inequalities (GFIIs), the hierarchical Lyapunov-Krasovskii functional (LKF) candidates are constructed. Then, the GFIIs are applied for the approximation of the integral quadratic terms, which will introduce the delay related nonlinear terms in the LKF differential. Next, the novel adjusted matrix-valued high and odd degree polynomial negative definite conditions (NDCs) are provided to acquire the hierarchical linear matrix inequality (LMI) conditions and cope with the nonlinear terms introduced by the GFIIs. Eventually, the advantages of the obtained stability conditions are checked through some numeric examples.

A flexible membership-dependent functional method to stability and stabilization for T-S fuzzy systems with interval time-varying delay

In this paper, the stability and stabilization problems for T-S fuzzy delayed systems is studied. A flexible membership-dependent Lyapunov functional (FMDLF) is constructed to fully utilize the information of time-varying delay and fuzzy membership functions (FMFs). Different from some exiting ones, the upper and lower limits of the integral terms in the FMDLF are adjustable. By first introducing exponential gains in reciprocally convex inequality, an exponential-type reciprocally convex inequality (ETRCI) is developed to estimate the FMDLF, which generates some existing results. Based on the FMDLF and ETRCI, a novel stability criterion is obtained. By using a decoupling technique, the corresponding controller design problem is solved. Importantly, the dimensions of the solution space increase since the constraints on slack matrices in some previous studies are eliminated. The effectiveness of the proposed results can be demonstrated by some examples.

Output synchronization of heterogeneous multi-agent systems based on the distributed continuous-discrete state observer

The output synchronization of heterogeneous multi-agent systems is investigated in this note based on the leader–follower architecture. We first propose a distributed continuous-discrete state observer for each follower to continuously estimate the state of the leader only utilizing the discrete samples. The local estimates of the observer are sampled and updated at the periodic sampling time, while the local samples are transmitted aperiodically between neighboring agents. Thus, it allows the asynchronous intermittent communication in the network with the interval time-varying communication delay. Then, the distributed controller is constructed based on the distributed observer to achieve exponential output synchronization. A numerical example is used to illustrate the validity of the theoretical results.

A Sufficient Condition on Polynomial Inequalities and its Application to Interval Time-Varying Delay Systems

This article examines the stability problem of systems with interval time-varying delays. In the derivation of Lyapunov–Krasovskii functional (LKF), non-convex higher-degree polynomials may arise with respect to interval time-varying delays, making it difficult to determine the negative definiteness of LKF’s derivative. This study was conducted to obtain stability conditions that can be described as linear matrix inequalities (LMIs). By considering the idea of matrix transition and introducing the delay-dependent augmented vector, a novel higher-degree polynomial inequality is proposed under the condition that the lower bound of the polynomial function variable is non-zero, which encompasses the existing lemmas as its special cases. Then, benefiting from this inequality, a stability criterion is derived in terms of LMIs. Finally, several typical examples are presented to verify the availability and strength of the stability condition.

Further improvement of finite-time boundedness based nonfragile state feedback control for generalized neural networks with mixed interval time-varying delays via a new integral inequality

This article investigates new delay-dependent finite-time boundedness for generalized neural networks (GNNs) with mixed-interval time-varying delays based on nonfragile feedback control to achieve the improved stability criterion. We also propose a new integral inequality with an exponential function to estimate the derivative of the Lyapunov–Krasovskii functional (LKF). Furthermore, the well-known Wirtinger’s inequality is a particular case of the new integral inequality. Using a toolbox optimization in MATLAB, we derive and solve new delay-dependent conditions in terms of linear matrix inequalities (LMIs). Additionally, we give three numerical examples to show the advantages of our obtained methods. The examples can apply the continuous time-varying delays that do not need to be differentiable. One of them presents the benchmark problem’s real-world application, which is a four-tank system.

Static anti-windup compensator design for locally Lipschitz systems under input and output delays.

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints.

Sensor networks with distributed event-triggered scheme for T–S fuzzy system with dissipativity analysis

In this article, the problem of distributed extended dissipativity consensus filtering over the mobile sensor environment in which each sensor communicates through an event is investigated. We address the fuzzy filtering problem through a unified approach that considers H∞, L2−L∞ and dissipative performance constraints. The event-triggering scheme is determined by event-based data processors (EDPs), which determine whether the sampled–data needs to be transmitted. A filter built on event data is applied at each node based on the collected samples from a sensor and its neighbors. By transforming it into an error system with an interval time-varying delay, the distributed event-triggered dissipative consensus filtering problem is solved. A new fuzzy Lyapunov–Krasovskii approach is derived to solve the filtering problem in the form of Linear Matrix Inequality (LMIs). Finally, using an engineering example, a unified algorithm for co-designed filter gains as well as for threshold parameters at the event condition is presented.

H$_{\infty }$ filter design for nonlinear systems with interval time-varying delay via T-S fuzzy models

H$_{\infty }$ filter design for nonlinear systems with interval time-varying delay via T-S fuzzy models

Novel stability analysis methods for generalized neural networks with interval time-varying delay

This paper deals with the stability analysis of generalized neural networks (GNN) with interval time-varying delay, and some novel stability criteria are proposed. For the delay, more specifically, it has the upper and lower bounds but the information of its derivative is unknown (or itself is not differentiable). Firstly, a new Lyapunov-Krasovskii functional (LKF) is constructed to obtain the less conservative stability results. Then, in order to cooperate with the introduced LKF, the free-matrix-based inequality (FMBI) is employed in the estimation of the integral quadratic terms. Next, by utilizing the new negative definite conditions (NDCs) of matrix-valued cubic polynomials, the stability conditions are presented in the form of linear matrix inequalities (LMIs). In addition, in the establishment process of these conditions, no extra state variables are introduced and the positive definite constraint on the LKF is relaxed. Finally, the validity and advantages of the proposed conditions are illustrated with some classical numerical examples.

Stability analysis of load frequency control for power systems with interval time-varying delays

This study investigates the stability problem of load frequency control (LFC) for power systems with interval time-varying delays. The two categories of time delays, the lower bound being zero and non-zero, are considered. The systems can be described as time delay systems of load disturbances. First, an augmented Lyapunov–Krasovskii functional (LKF) is constructed. Some delay-dependent nonintegral terms and single integral terms are additionally introduced to make full use of the information on the system state variables and the time-varying delays. Second, to overcome the problem of nonlinear inequalities caused by the augmented LKF, the nonlinear inequalities are converted into linear matrix inequalities (LMIs) by applying the new negative definite inequality equivalence transformation lemma, which can be solved easily by the MATLAB LMI toolbox. A new stability criterion is presented by applying the Lyapunov stability theory. The stability criterion is less conservative than some existing literature studies, which further improves the stability margin for the power systems based on LFC. Finally, some numerical examples are given to show the effectiveness of the proposed method and the superiority of the results.

New stability criteria for systems with an interval time-varying delay

<abstract><p>This paper studies the stability analysis of systems with an interval time-varying delay. First, some new integral inequalities are introduced. Second, based on these new integral inequalities, some less conservative stability criteria are introduced in terms of the linear matrix inequalities. Finally, the merits of the stability criteria are shown via two numerical examples.</p></abstract>

Admissibility Analysis and Control for Discrete-Time Singular Systems with Interval Time-Varying Delay

This paper mainly investigates an admissibility analysis and controller design problem for an uncertain discrete-time singular system with delayed states. The time-varying delay is within an interval whose lower bound may be greater than zero. Using a modified finite sum inequality and choosing a suitable Lyapunov-Krasovskii function, we derive a set of LMI-based sufficient delay-dependent conditions for the admissibility analysis and controller synthesis problem, respectively. In the end, a numerical example shows the effectiveness and validity of the proposed approach.

Stability Analysis of Linear Systems With Interval Time-Varying Delay

Stability Analysis of Linear Systems With Interval Time-Varying Delay

Stability Analysis of Two-Area LFC Power Systems With Two Additive Interval Time-Varying Delays

Stability Analysis of Two-Area LFC Power Systems With Two Additive Interval Time-Varying Delays

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>