Mode-dependent stochastic synchronization criteria for Markovian hybrid neural networks with random coupling strengths

This paper is concerned with the stochastic synchronization problem for a class of Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time-delays in the mean square. First, a novel inequality is established which is a double integral form of the Wirtinger-based integral inequality. Next, by employing a novel augmented Lyapunov–Krasovskii functional (LKF) with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent Markovian hybrid coupled neural networks. Finally, a numerical example with simulation is provided to illustrate the effectiveness of the presented criteria.     

Dissipative filtering for singular Markov jump systems with generally uncertain transition rates via new integral inequality approach

This paper considers the problem of dissipative filtering problem for singular Markov jump systems with time-varying delay and generally uncertain transition rates. Firstly, by tuning the improved integral inequality and Wirtinger-based integral inequalities, a sufficient condition is derived to guarantee that the considered system is regular, impulse-free, stochastically stable with the dissipation performance. Then, based on the derived condition, and applying linear matrix inequalities (LMIs) techniques, the filter is synthesized. Finally, some numerical examples are given to illustrate the effectiveness of the obtained theoretic results.     

Novel delay-partitioning approaches to stability analysis for uncertain Lur’e systems with time-varying delays

This work deals with the problem of absolute stability analysis for a class of uncertain Lur’e systems with time-varying delays. Novel delay-partitioning approaches are presented, which are dividing the variation interval of the delay into three subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on each of the obtained subintervals which can efficiently make use of the information of the delay and relate to the reciprocally convex combination technique and the Wirtinger-based integral inequality method. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). The merit of the proposed criteria lies in their less conservativeness and lower numerical complexity than relative literature. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.     

Improved stabilization criteria for fuzzy systems under variable sampling

This paper investigates the problem of stabilization for fuzzy sampled-data systems with variable sampling. A novel Lyapunov–Krasovskii functional (LKF) is introduced to the fuzzy systems. The benefit of the new approach is that the LKF develops more information about actual sampling pattern of the fuzzy sampled-data systems. In addition, some symmetric matrices involved in the LKF are not required to be positive definite. Based on a recently introduced Wirtinger-based integral inequality that has been shown to be less conservative than Jensen’s inequality, much less conservative stabilization conditions are obtained. Then, the corresponding sampled-data controller can be synthesized by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the feasibility and effectiveness of the proposed method.     

Extended dissipative analysis for aircraft flight control systems with random nonlinear actuator fault via non-fragile sampled-data control

This paper addresses the issue of reliable feedback control of an uncertain aircraft flight control systems with disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which is described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov–Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the aircraft flight control systems not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique.     

Exponential synchronization of the switched uncertain neural networks with mixed delays based on sampled-data control

The synchronization for a class of switched uncertain neural networks (NNs) with mixed delays and sampled-data control is researched in this paper. When a switching signal occurs in a sampling interval, the controller cannot switch until the next sampling instant. There is a mismatch between the system and the controller. Thus, we devise the control strategy to guarantee that the switched NNs can be synchronized. The proposed Lyapunov-Krasovskii functional (LKF) can make full use of system information. By use of an improved integral inequality, some sufficient stability conditions formed by linear matrix inequalities (LMIs) are derived for the synchronization of switched NNs. Average dwell time (ADT) is obtained as a form of inequality that includes the sampling interval. At last, the feasibility of the proposed method is proved by some numerical examples.     

Non-fragile sampled-data stabilization analysis for linear systems with probabilistic time-varying delays

This paper deals with the problem of non-fragile sampled-data stabilization analysis for a class of linear systems with probabilistic time-varying delays via new double integral inequality approach. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical approaches, a new double integral inequality (NDII) is developed. Then, to demonstrate the merits of the proposed inequality, an appropriate Lyapunov–Krasovskii functional (LKF) is constructed with some augmented delay-dependent terms. By employing integral inequalities, an enhanced stability criterion for the concerned system model is derived in terms of linear matrix inequalities (LMIs). Finally, three benchmark illustrative examples are given to validate the effectiveness and advantages of the proposed results.     

Robust stability criteria for uncertain systems with interval time-varying delay based on multi-integral functional approach

This paper is concerned with the robust stability analysis for uncertain systems with interval time-varying delay. In order to make full use of the delay information, a novel Lyapunov–Krasovskii functional (LKF) containing single, double, triple and quadruple integral terms is introduced, and a triple-integral state variable is also used. Then, by using the Wirtinger-based single and double integral inequality, introducing some positive scalars, the derivative of the constructed LKF is estimated more accurately. As a result, some stability criteria are derived, which have less conservatism and decision variables. Numerical examples are also given to show the effectiveness of the proposed method.     

Discrete Legendre polynomials-based inequality for stability of time-varying delayed systems

This paper proposes Discrete Legendre Polynomial(DLP)-based inequality by solving the best weighted approximation of a given time series. The proposed inequality could significantly reduce the conservativeness in stability analysis of systems with constant or interval time-varying delays. Also former well-known integral inequities, such as discrete Jensen inequality, discrete Wirtinger-based inequality, are both included in the proposed DLP-based inequality as special cases with lower-order approximation. Stability criterion with less conservatism is then developed for both constant and time-varying delayed systems. Several numerical examples are given to demonstrate the effectiveness and benefit of the proposed method.     

Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction–diffusion terms via sampled-data control

This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.     

Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays.     

Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control

In this paper, we concern the finite-time synchronization problem for delayed dynamical networks via aperiodically intermittent control. Compared with some correspondingly previous results, the intermittent control can be aperiodic which is more general. Moreover, by establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realize finite-time synchronization for delay complex networks. Additionally, as a special case, some sufficient conditions ensuring the finite-time synchronization for a class of coupled neural network are obtained. It is worth noting that the convergence time is carefully discussed and does not depend on control widths or rest widths for the proposed aperiodically intermittent control. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

Two novel general summation inequalities to discrete-time systems with time-varying delay

This paper presents two novel general summation inequalities, respectively, in the upper and lower discrete regions. Thanks to the orthogonal polynomials defined in different inner spaces, various concrete single/multiple summation inequalities are obtained from the two general summation inequalities, which include almost all of the existing summation inequalities, e.g., the Jensen, the Wirtinger-based and the auxiliary function-based summation inequalities. Based on the new summation inequalities, a less conservative stability condition is derived for discrete-time systems with time-varying delay. Numerical examples are given to show the effectiveness of the proposed approach.     

Improved approaches on adaptive event-triggered output feedback control of networked control systems

This paper studies the static output-feedback control in a class of networked control systems. Different from the existing results, the transmission of control signals is based on a novel adaptive event-triggered scheme, where the adaptive thresholds depend on the dynamic error of the system rather than predetermined constants as the traditional ones. The amount of the releasing data is regulated by the adaptive thresholds that play an essential role in decision of whether releasing the sampled data or not. Through fully using the information on network-induced delay and introducing two adjusting parameters, an augmented Lyapunov–Krasovskii (L–K) functional is constructed. Especially, some novel Wirtinger-based integral inequalities are utilized to reconsider those previously ignored information, which can help reduce the conservatism. Furthermore, a novel constructive method is developed to obtain the controller gain by solving the achieved linear matrix inequalities (LMIs). Finally, three numerical examples are given to illustrate the efficiency of the presented results.     

Guaranteed cost synchronization for second-order wireless sensor networks with given cost budgets

The current paper addresses leader-following guaranteed cost synchronization with the cost budget given previously for the second-order wireless sensor networks. The published researches on guaranteed cost synchronization design criteria usually are based on the linear matrix inequality (LMI) techniques and cannot take the cost budget given previously into consideration. Firstly, the current paper proposes a guaranteed cost synchronization protocol, which can realize the tradeoff design between the battery power consumption and the synchronization regulation performance. Secondly, for the case without the given cost budget, sufficient conditions for leader-following guaranteed cost synchronization are presented and an upper bound of the cost function is shown. Thirdly, for the case that the cost budget is given previously, the criterion for leader-following guaranteed cost synchronization is proposed. Especially, the value ranges of control gains in these criteria are determined, which means that the existence of control gains in synchronization criteria can be guaranteed, but the LMI techniques can only determine the gain matrix and cannot give the value ranges of control gains. Moreover, these criteria are only associated with the minimum nonzero eigenvalue and the maximum eigenvalue, which can ensure the scalability of the wireless sensor networks. Finally, numerical simulations are given to illustrate theoretical results.     

A generalized multiple-integral inequality and its application on stability analysis for time-varying delay systems

This paper is concerned with the stability analysis of time-delay systems. Lyapunov–Krasovskii functional method is utilized to obtain stability criteria in the form of linear matrix inequalities. The main purpose is to obtain less conservative stability criteria by reducing the estimation gap of the time derivative of the constructed Lyapunov–Krasovskii functional. First, a generalized multiple-integral inequality is put forward based on Schur complement lemma. Then, some special cases of the proposed generalized multiple-integral inequality are given to estimate single and double integral terms in the derivative of Lyapunov–Krasovskii functional. Furthermore, less conservative stability criteria are derived. Finally, three examples are given to illustrate the improvement of the proposed criteria.     

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.     

Delayed proportional-integral control for offshore steel jacket platforms

This paper is concerned with the problem of delayed proportional-integral control of an offshore platform subject to self-excited nonlinear hydrodynamic force. By using current and distributed delayed states, a delayed proportional-integral controller is designed to stabilize the offshore platform. Under such a controller, the closed-loop system of the offshore platform is modeled as a nonlinear system with discrete and distributed delays, which allows us to employ the Lyapnov–Krasovskii functional method to analyze its asymptotic stability. Since an affine Wirtinger-based inequality is exploited to estimate the derivative of the Lyapunov–Krasovskii functional, a new stability criterion for the closed-loop system is derived, based on which, suitable control gains can be designed provided that a set of linear matrix inequalities are feasible. It is found through simulation results that the proposed control scheme can improve the control performance remarkably. Moreover, (i) compared with the existing delay-free controllers, the proposed controller can reduce the required control force and the oscillation amplitudes of the platform significantly; and (ii) compared with several delayed controllers, the proposed controller requires less control cost.     

Passivity analysis of coupled neural networks with reaction–diffusion terms and mixed delays

In this paper, we intend to discuss the passivity of coupled neural networks (NNs) with reaction–diffusion terms and mixed delays. By constructing appropriate Lyapunov functional, and with the help of liner matrix inequalities, some inequality techniques, several sufficient conditions are derived to guarantee the output strictly passive, input strictly passive, passive of the proposed neural network model. Then, a stability criterion is presented according to the obtained passivity results. Moreover, the proposed neural network model herein is more general than some recent studies, which can improve and enrich the previous research results. Finally, a numerical example is presented to show the effectiveness of the theoretical criteria.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.