Time-varying Delay Components Research Articles

Input-to-state stability of stochastic Markovian jump genetic regulatory networks

The development of gene circuits in logic modules that start enormous output distributions with low signal-to-noise ratios is a difficult problem in engineering. As a result, the gene model depicts the transcription and translation of a single gene produced in the modification of noise in isolated logic modules. Our goal is to construct such networks with all types of connectivity. Further, the impacts of noise on further complex genetic networks have been investigated using stochastic gene models. Using this information as a foundation, our research investigates the input-to-state stability investigation for stochastic Markovian jump genetic regulatory networks with time-varying delay components. The goal of this article is to develop genetic networks with temporal delays, which are crucial for genetic regulation because slow biochemical processes like gene transcription and translation need time to occur. Additionally, the Markovian chain is essential for demonstrating how a system shifts from one mode to another with known transition probabilities. In the stochastic case, some complex systems with random disturbance will occur. Due to this significance the genetic regulatory network with stochastic case is applied to identify the complex behaviour among genes and proteins of the micro perspective. By establishing the Lyapunov functional with Ito’s and Dynkin’s formula, new stability conditions are derived and which is effectively solved by MATLAB toolbox. The efficiency of the suggested technique is demonstrated using a numerical example.

Delay-Dependent Switching Approaches for Stability Analysis of Two Additive Time-Varying Delay Neural Networks.

This article analyzes the exponentially stable problem of neural networks (NNs) with two additive time-varying delay components. Disparate from the previous solutions on this similar model, switching ideas, that divide the time-varying delay intervals and treat the small intervals as switching signals, are introduced to transfer the studied problem into a switching problem. Besides, delay-dependent switching adjustment indicators are proposed to construct a novel set of augmented multiple Lyapunov-Krasovskii functionals (LKFs) that not only satisfy the switching condition but also make the suitable delay-dependent integral items be in the each corresponding LKF based on each switching mode. Combined with some switching techniques, some less conservativeness stability criteria with different numbers of switching modes are obtained. In the end, two simulation examples are performed to demonstrate the effectiveness and efficiency of the presented methods comparing other available ones.

A binary quadratic function negative‐determination lemma and its application to stability analysis of systems with two additive time‐varying delay components

This paper concentrates on the stability problem of systems with two additive time-varying delay components. For the construction of Lyapunov–Krasovskii functional (LKF), in the case that the introduced augmented vector contains the double integral term of the state vector, a special form of the binary quadratic function with respect to two time-varying delays has often been introduced into the derivative of the LKF. In order to determine the negative definiteness of such function, by making full use of the idea of partial differential, the convex/concave property and the slope characteristic of tangent lines of the binary quadratic function, a binary quadratic function negative-determination lemma is proposed in the case of the pluses or minuses of quadratic coefficients are unknown. Then, the obtained stability criterion in the form of linear matrix inequality shows a greater advantage than the previous criteria since not only some advanced techniques are employed to treat some integral terms, but also the proposed lemma is employed to deal with quadratic terms in functional derivative. Finally, a typical example is given to verify the superiority of the derived criterion.

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving uncertainties as well as time-varying delay components. The requisite of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is extended dissipative having external disturbance and unpredictable fragility performance. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), the sufficient conditions for the extended dissipativity performance of the error system obtained by means of the proposed DNNs and its estimator which includes the $$H_{\infty }$$ performance, $$L_{2}-L_{\infty }$$ performance, passivity and dissipativity performance in a unified framework. The established theoretical results are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical softwares. In order to analyze the applicability and effectiveness of the proposed theoretical results, numerical examples including a quadruple tank process (QTP) system model have been illustrated with simulation results.

New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

This paper focuses on the stability problems of continuous linear systems with two additive time-varying delay components. Firstly, an effective and simple Lyapunov–Krasovskii functional (LKF) is established, which not only takes adequate information of delay components and their upper bounds into consideration but also establishes a simpler form to decrease the computational complexity. Secondly, an improved delay-dependent stability criterion together with its corollary is obtained by employing the generalized free-weighting-matrix-based (GFWM-based) inequality and some other techniques to calculate the derivative of the constructed LKF, which will further reduce the introduced estimation error and make the criteria less conservative. Lastly, a numerical example is presented to illustrate the less conservatism and lower computational complexity of the derived results.

Improved Delay-dependent Stability Criteria for Networked Control System with Two Additive Input Delays

This paper is concerned with stability criteria of networked control system with two additive time-varying delay components. Firstly, by separating the whole delay interval into subintervals and using a new inequality in combination with convex polyhedron method, a less conservative criterion is proposed and an approach of stabilization controller design is given based on the obtained criterion. Secondly, a congruent condition and an extended condition with the same allowable delay upper bound are respectively deduced by using two different inequalities. Finally, some numerical examples are presented to illustrate the effectiveness of the obtained method.

State estimation for neural networks with two additive time-varying delay components using delay-product-type augmented Lyapunov–Krasovskii functionals

This paper focuses on the state estimation issue of neural networks with two additive time-varying delay components. By constructing a suitable augmented Lyapunov–Krasovskii functional, more time delay information is considered. Using the recently developed reciprocally convex inequality, some reciprocally convex combinations can be estimated more closely. The design conditions of state estimators are expressed as linear matrix inequalities (LMIs). The delay-product-type Lyapunov–Krasovskii functional is used to further reduce the conservativeness. With the help of state estimation method, the stability conditions of neural networks with two additive time-varying delay components are also developed. Finally, two numerical examples widely used in the literature show the effectiveness of the proposed method.

Stability analysis of systems with two additive time-varying delay components via an improved delay interconnection Lyapunov–Krasovskii functional

This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.

Sampled-Data State Estimation for Neural Networks with Additive Time–Varying Delays

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampled-data control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen’s inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

Robust <inline-formula> <tex-math notation="LaTeX">$H_{\infty}$ </tex-math> </inline-formula> Control of Lurie Nonlinear Stochastic Network Control Systems With Multiple Additive Time-Varying Delay Components

In order to further solve the stability problem in the actual network control systems, this paper first simultaneously considers the controlled object system delay and network time delay in the Lurie nonlinear stochastic network control systems. Among them, the controlled object system delay is multi-time delay and the network time delay is two additive time-varying delay component. The proposing of the two additive time-varying delay components in network control systems has advantages in producing less conservatism over the previous one with a combined delay. By employing the method of improved free weighting matrix and constructing a Lyapunov–Krasovskii functional, less conservative robust $H_{\infty }$ stability criterion is established and the controller is designed for the system in this paper. Some numerical examples are given to demonstrate the applicability of the proposed method.

Sampled-Data State Estimation of Neutral Type Neural Networks with Mixed Time-Varying Delays

In this paper, we consider the problem of sampled-data control for neutral type neural networks with mixed time-varying delay components. A proper Lyapunov–Krasovskii functional is constructed by dividing the discrete and neutral delay intervals with triple and quadruplex integral terms. By employing the input delay approach, the sampling period is converted into a bounded time-vary delay in the estimation error dynamic. By employing Lyapunov-functional approach and utilizing LMI technique, sufficient conditions have been derived to guarantee that the estimation error dynamics is asymptotically stable. A numerical example is provided to illustrate the usefulness and effectiveness of the obtained results.

New Delay-Dependent Stability Criteria for Impulsive Neural Networks with Additive Time-Varying Delay Components and Leakage Term

This work is concerned with the delay-dependent stability problem for uncertain impulsive neural networks (NNs) with additive time-varying delay components and leakage term. We construct a newly augmented Lyapunov–Krasovskii (L–K) functional which contains triple and four integral terms and then utilizing free-matrix-based integral inequality to bound the derivative of the Lyapunov–Krasovskii functional. Some sufficient conditions are derived to assure the delay-dependent stability of the impulsive NNs by the linear matrix inequality, which is less conservative than some existing results and can be readily verified by the convex optimization algorithms. In addition, some information of activation function ignored in previous works has been taken into account in the resulting condition. In the end, three numerical examples are provided to illustrate the effectiveness of the proposed criteria.

Non-fragile mixed H-infinity and passivity control for neural networks with successive time-varying delay components

This paper is concerned with the problem of nonfragile mixed H∞ and passivity control for neural networks with successive time-varying delay components. We construct a suitable Lyapunov–Krasovskii function with triple and quadruple integral terms then utilizing Jensen's lemma and Wirtinger-type inequality technique. Some sufficient conditions are presented for the existence of nonfragile mixed H∞ and passivity performance criterions. The expressions for the nonfragile controller can be obtained by solving a set of linear matrix inequality. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed method.

New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays

This paper examines the problem of asymptotic stability criteria for Markovian jump generalized neural networks with successive time-varying delay components. Generalized neural networks consist of a finite number of modes, which may jump from one mode to another according to a Markovian chain with known transition probability. By constructing novel augmented Lyapunov–Krasovskii functionals (LKFs) with triple integral terms that contain more and more information on the state vectors of the NNs, the upper bound of the successive time-varying delays is formulated. By employing a new integral inequality technique, free-weighting matrix-based integral inequality approach, and Wirtinger double integral inequality technique and that is combined with the reciprocally convex combination approach to estimate the single and double integral terms in the time derivative of the LKFs, a new set of delay-dependent conditions for the asymptotic stability of the considered NNs are represented in the form of linear matrix inequalities. Finally, five numerical examples are given to verify the effectiveness of the proposed approach with a four-tank benchmark real-world problem.

Improved results on state feedback stabilization for a networked control system with additive time-varying delay components' controller

This paper investigates the problems of stability and stabilization for a networked control system (NCS) with additive time-varying delay components' controller. Firstly, stability of a NCS with additive time-varying delays is investigated. A novel approach with free parameters is proposed. By constructing a new Lyapunov-Krasovskii functional (LKF) with two free parameters, stability criteria are obtained. The obtained stability criteria depend not only on upper bounds of delays but also free parameters. In addition, input-output method is extended to study the stability problem for the NCS. Compared with other approaches such as input-output method, the free-parameter approach is more flexible and effective in reducing the conservatism. Then, based on the stability results, a state feedback controller is designed to guarantee the asymptotically stable of the closed-loop systems. Finally, numerical examples are provided to show the effectiveness and less conservatism of the proposed results.

Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality

This paper is concerned with the stability analysis of Lur’e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays

In this paper, the stability of the system with two additive time-varying delay components is studied and improved stability condition is obtained. It firstly establishes two novel integral inequalities, which are better than the same type inequalities found in the literature. Secondly, a new constructed Lyapunov functional is constructed based on the additive time-varying delays property. Following two steps to handle the Lyapunov functional, the delay-dependent stability condition is obtained which in terms of linear matrix inequalities. Finally, two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results.

Novel Lebesgue-integral-based approach to improved results for neural networks with additive time-varying delay components

In this paper, we propose a novel Lebesgue-integral-based approach to investigate the stability for neural networks with additive time-varying delay components. Based on the Lebesgue integral theory, a new Lyapunov–Krasovskii functional (LKF), which involves Lebesgue integral terms, is constructed, and the corresponding stability theorem is derived. More information on the neuron activation functions and fewer matrix variables are involved in the constructed LKF. Then, on the basis of the above method, an improved stability criterion is developed. Compared with the existing results, the derived stability condition is with less conservatism and computational burden. Moreover, the obtained criterion is extended to study the system with a single time-varying delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Passivity-based non-fragile control for Markovian jump delayed systems via stochastic sampling

ABSTRACTThis paper studies the problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling. The Markovian jumping parameters, appearing in the connection weight matrices and in two additive time-varying delay components, are considered to be different. The controller is assumed to have either additive or multiplicative norm-bounded uncertainties. The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional. This functional fully utilises the sawtooth structure characteristics of the sampling input delay. By using the matrix decomposition method and some newly inequalities, sufficient conditions are obtained to guarantee that for all admissible uncertainties the system is robustly stochastically passive. Illustrative examples are provided to show the effectiveness of the results.

Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

In this paper, the global asymptotic stability of memristive bidirectional associative memory neural networks with leakage delay and two additive time-varying delays is firstly studied. Then, we propose a novel sampled-data feedback controller to guarantee the synchronization of system based on drive/response concept. In particular, taking full advantage of the input delay approach, the Lyapunov function method and the Jensen’s inequality theory, several sufficient conditions are obtained. Finally, two numerical simulation examples show the effectiveness of the designed sampled-data control strategy. Furthermore, our results can be applied to simulate the associative memory function of brain-like robots, large-scale information storage, etc.