Delay-dependent Stability Criteria Research Articles

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay

This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay. A new delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed. Based on the LKF and by employing a generalized free-matrix-based integral inequality, less conservative delay-dependent stability criteria are obtained. Finally, two well-known numerical examples are used to confirm the effectiveness and the superiority of the presented stability criteria.

Delay-Dependent Criteria for Global Exponential Stability of Time-Varying Delayed Fuzzy Inertial Neural Networks

This paper is mainly concerned with global exponential stability of time-varying delayed fuzzy inertial neural networks. Different from previous approaches of variable transformation, we use non-reduced order method. Different from previous non-reduced order method used to investigate the inertial neural networks without time-varying delays, we take the time-varying delayed effects into account. By constructing a modified delay-dependent Lyapunov functional and inequality technique, delay-dependent criteria stated with simple algebraic inequalities are given in order to ensure the global exponential stability for the addressed delayed fuzzy inertial neural network model. The approach applied can provide a new method to study the fuzzy inertial neural networks with time delays via non-reduced order method. Some previous works in the literature are extend and complement. Finally, numerical examples with simulations are presented to make comparisons between the system with delays and without delays, and further demonstrate the validity and originality of the proposed approach.

An augmented delays-dependent region partitioning approach for recurrent neural networks with multiple time-varying delays

This paper investigates the global asymptotic stability problem of recurrent neural networks with multiple time-varying delays. First, to make full use of the relationship between all delayed states x(t-τi)(i=1,…,N) and current state x(t), an augmented delays-dependent region partitioning (ADRP) approach is proposed. Then combining Wirtinger-based integral inequality and the reciprocally convex approach, two delay-dependent stability criteria with less conservatism are developed. Finally, two numerical simulations are shown to verify the effectiveness and the feasibility.

Improved Delay-Dependent Stability Criterion for Genetic Regulatory Networks with Interval Time-Varying Delays via New Lyapunov Functionals

In this work, the stability analysis problem of the genetic regulatory networks (GRNs) with interval time-varying delays is presented. In the previous works, the constructions of Lyapunov functional have usually been in simple Lyapunov functional, augmented Lyapunov functional, and multiple integral Lyapunov functional. Therefore, we introduce new Lyapunov functionals expressed in terms of delay product functions. New delay-dependent sufficient conditions for the genetic regulatory networks (GRNs) are established in the terms of linear matrix inequalities (LMIS). In addition, a numerical example is provided to illustrate the effectiveness of the theoretical results.

Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method

This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination and a relaxed quadratic function negative-determination are employed. Based on these methods and the augmented LKF, a less conservative delay-dependent stability criterion for GNN with a fast-varying delay is presented. Finally, some numerical examples are given to demonstrate the effective superiority of the proposed criterion.

Delay-dependent criteria for periodicity and exponential stability of inertial neural networks with time-varying delays

This paper mainly studies the periodicity and exponential stability for a class of inertial neural networks (INNs) with time-varying delays. Without utilizing standard reduced-order transformation, by using the continuation theorem and Cauchy–Schwarz inequality, delay-dependent criteria shown by some algebraic inequalities are derived to ensure the existence of periodic solutions. Furthermore, by means of the fundamental inequality and constructing a modified delay-dependent Lyapunov functional, global exponential stability analysis is obtained based on the derived delay-dependent criteria. In comparison with the reduced order approach applied to the INNs and delay-independent criteria provided for the INNs in the existed literatures, the results obtained in this paper are new. Finally, numerical simulations are carried out to verify the main results.

Event-triggered [formula omitted] control for active seat suspension systems based on relaxed conditions for stability

An event-triggered H∞ controller is designed for an active seat suspension in this paper, where the continuous event-trigger scheme is applied to transfer the dynamic system states to the controller only at event-triggered time instants. Delay-dependent stability criteria in the form of linear matrix inequality (LMI) are presented to guarantee the asymptotic stability of the seat suspension system. One Lyapunov function is chosen where some matrices are introduced with relaxed conditions. Two tight inequalities are applied to prove the positive definiteness of the Lyapunov function and stability of the system, which reduces the conservatism of the system for the time delay to the controller. The proposed control method can reduce the workload of data transmission of the seat suspension system and work as a filter to remove the effect of noise, so it can decrease the precision requirement of the actuator, which can help to reduce the cost of the seat suspension. Both simulation and experimental results are presented to show the effectiveness of the proposed control method.

Stability analysis of network-controlled DC position servo system with time-delay

This paper presents a stability analysis of network-controlled direct current (DC) position servo system with time-delays (TDs). The usage of communication links and measurement devices in the network-controlled system involves a considerable amount of TDs. Those TDs would degrade the dynamic performance and causes instability to the DC position servo system. A less conservative delay-dependent stability (DDS) criterion is presented by using Lyapunov–Krasvoskii functional and linear matrix inequality techniques. The maximum allowable TD called delay margin (DM) is computed, which can be used to tune a proportional-integral (PI) controller of the DC position servo system. Two cases of TD are considered in this analysis: time-invariant and time-varying delays. The DDS approach is used to study the trade-off between the PI controller gains and the DMs. This approach together with numerical simulation gives the insightful trade-off between DM and dynamic performance of the system. Finally, the stability of the DC position servo system with PI controller is analysed in the presence of TD through the experimental setup.

Stability analysis of delayed neural network using new delay-product based functionals

This paper concerns with stability analysis of neural networks with time varying delay. Two new delay-product type functionals (DPFs) are developed by introducing new states in the augmented vector of delay-product term. Then using these DPFs, two new Lyapunov-Krasovskii functionals (LKFs) are constructed. Based on these LKFs, two delay-dependent stability criterion are obtained in the form of linear matrix inequalities. The effectiveness of the proposed criterion for delayed neural network is demonstrated by considering two examples.

A Novel Approach to Mean Square Exponential Stability of Stochastic Delay Differential Equations

We present a novel approach to the mean square exponential stability of stochastic delay differential equations. Consequently, some new explicit criteria for the mean square exponential stability of general nonlinear stochastic delay differential equations are derived. Both delay-independent and delay-dependent stability criteria are given, and illustrative examples are also provided.

Delay-dependent stability and hybrid [formula omitted]-gain analysis of linear impulsive time-delay systems: A continuous timer-dependent Lyapunov-like functional approach

This paper presents a new approach for analyzing delay-dependent stability and hybrid L2×l2-gain performance of linear impulsive delay systems. The new approach is inspired by the delay-partitioning method, the timer-dependent Lyapunov functional method, and the looped-functional method. In the delay-partitioning framework, a new type of timer-dependent Lyapunov functional is constructed, which depends on the partition on impulse intervals and also on impulse dynamics. Different from the previous discontinuous Lyapunov functionals, the introduced Lyapunov functional is continuous along the trajectories of the considered impulsive delay system. Consequently, two different problems of exponential stability and hybrid L2×l2-gain performance are tackled by using the same class of Lyapunov functionals. It is shown that the positive definiteness of this Lyapunov functional inside impulse intervals is not necessary for proving exponential stability. By use of new integral inequalities based techniques, delay-dependent criteria for exponential stability and finite hybrid L2×l2-gain are established in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach.

Stability criteria of quaternion-valued neutral-type delayed neural networks

Stability problem of quaternion-valued neutral-type delayed neural networks (QVNTDNNs) is researched in this paper. By utilizing homeomorphism principle, matrix inequality technique and Lyapunov method, both delay-independent and delay-dependent stability criteria are established in the form of linear matrix inequalities to pledge the existence, uniqueness and global stability of the equilibrium point of the considered QVNTDNNs. An example with simulations is given to manifest the validity of the exported results.

State estimation for discrete-time high-order neural networks with time-varying delays

This paper focuses on state estimation problem for discrete-time high-order neural networks with time-varying delays. First, the delay-dependent global exponential stability criterion of the error system is derived. Then, the state observer is designed by using the generalized inverse theory of matrices. Last, two numerical examples are given to illustrate the validity of the theoretical results. The method proposed in this paper has two advantages: (i) it is directly based on the definitions of global exponential stability and Moore–Penrose inverse of matrix, which avoids the construction of Lyapunov–Krasovskii functional; (ii) the obtained stability criteria contain only several simple matrix inequalities, which are easier to solve. More valuable, this paper fills in the gaps in designing state observers for discrete-time high-order neural network models.

A Novel Method for Stability Analysis of Time-Varying Delay Systems

The Lyapunov–Krasovskii functional (LKF) method is an effective tool to obtain delay-dependent stability criteria of time-varying delay systems. However, in the method, the requirement that there must exist an appropriate LKF for a system with a delay varying in a delay interval is too strict and may lead to considerable conservativeness. In order to get less conservative stability criteria, a novel stability analysis method called a delay-mode-based LKF (DMBLKF) method is first presented for nonlinear delay systems. Compared with the LKF method, the main advantage of the DMBLKF method lies in relaxing the aforementioned requirement and leading to a less conservative criterion in stability analysis. Then, with the help of the novel method, new stability criteria of linear delay systems are derived. Finally, the effectiveness of the proposed method and the obtained criteria is illustrated through two numerical examples.

New criteria for mean square exponential stability of stochastic delay differential equations

By a novel approach, we present several new criteria for the mean square exponential stability of general non-linear stochastic delay differential equations. Both delay-independent and delay-dependent stability criteria are provided. A discussion of the obtained results is given.

Improved delay-dependent stability criteria for linear systems with multiple time-varying delays

This paper concentrates on the stability analysis of continuous-time linear systems with multiple time-varying delays. The time-delays are assumed to be bounded and have or not lower and upper bounds on their time-derivative. Based on the Lyapunov-Krasovskii theory the proposed results formulated as linear matrix inequality conditions can verify the delay-intervals for which the system stability is preserved. The main results follow from developing new augmented Lyapunov-Krasovskii functionals that exploit the benefits of the Bessel-Legendre-based integral inequality and the reciprocally convex approach. Also, the proposed functionals allow us to take advantage of the relationships between the current and delayed states. As a result, the proposed stability conditions outperformed similar existing ones in all numerical tests accomplished in this paper.

Enhanced stability results for generalized neural networks with time-varying delay

This paper deals with the stability analysis problem for generalized neural network with time-varying delay. A proper Lyapunov-Krasovskii functional (LKF) with novel delay-product-dependent term is constructed, which fully considers the features of the improved Jensen integral inequality. Based on the new proposed LKF and a more general integral inequality issued from the improved Jensen one, an enhanced delay-dependent stability criterion is developed in terms of linear matrix inequality (LMI). Furthermore, a more refined stability criterion is established by relaxing the positive definiteness of the LKF. The effectiveness of the theoretical results are demonstrated by four numerical examples.

A Delay-Dependent Approach to Finite-Time H∞ Control of Nonlinear Descriptor Systems with State Delay via Observer-Based Control

This paper proposes a finite-time observer-based controller for time-delay descriptor systems with time-varying disturbances, model uncertainties, and one-sided Lipschitz nonlinearities. For this purpose, first, a nonlinear descriptor observer is designed, and the observer error system is calculated. Then, the observer-based control law is proposed to provide the conditions for robust stabilization of the closed-loop descriptor system by selecting an appropriate Lyapunov–Krasovskii functional. According to the delay-dependent stability criterion, LMI-based sufficient conditions are derived and the gains of the controller and the observer are calculated. The proposed controller guarantees the finite-time boundedness and H∞ disturbance attenuation of the closed-loop descriptor system. Finally, the effectiveness of the proposed technique is investigated through computer simulations.

Delay-dependent stability criteria of delayed positive systems with uncertain control inputs: Application in mosquito-borne morbidities control

This note pays precise attention to derive the γ-exponential stability results of positive delayed systems via non-fragile control. By using Lyapunov–Krasovskii theory some necessary conditions are derived. Moreover, by using results from spectrum analysis the sufficient conditions for positive delayed systems with non-fragile control are analyzed. Our main intension is to locate the ideal application of this type of systems. In later part of this paper, the novel mathematical model which describes the life stages of Aedes Aegypti mosquitoes is proposed. In that model, the life shorting bacteria called Wolbachia is used as a biological control. By moderately thinking about the uncertain conditions in the biological control we implemented the non-fragile control. By applying the proposed results the γ-exponential stability of this population system is derived. Finally, some numerical examples are provided to expose the effectiveness of our predominant results.