Improved stability criteria for sampled-data systems using modified free weighting matrix

This paper investigates the stability analysis of sampled-data systems in the looped-functional framework. A modified free-weighting matrix inequality with quadratic-type is proposed to reduce conservatism of the integral term. Based on new looped-functional, improved conditions are derived in terms of linear matrix inequalities (LMIs) by utilizing the proposed integral inequality. Numerical examples show the superiority of the proposed condition through comparisons with the most recent results.     

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 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.     

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.     

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.     

State quantized sampled-data control design for complex-valued memristive neural networks

In this paper, several resultful control schemes based on data quantization are proposed for complex-valued memristive neural networks (CVMNNs). Firstly, considering the finite communication resources and the interference of failures to the system, a state quantized sampled-data controller (SQSDC) is designed for CVMNNs. Next, taking the interference of gain fluctuations into account, a non-fragile sampled-data control (SDC) law is proposed for CVMNNs in the framework of data quantification. In order to full capture more inner sampling information, a newly Lyapunov-Krasovskii function (LKF) is constructed on the basis of the proposed triple integral inequality. After that, in the framework of taking full advantage of the property of Bessel-Legendre inequality, a time-dependent discontinuous LKF (TDDLKF) is proposed for CVMNNs with SQSDC. Based on the useful LKF, several stability criteria are established. Finally, the numerical simulations are provided to substantiate the validity and less conservatism of the proposed schemes.     

Event triggered reliable synchronization of semi-Markovian jumping complex dynamical networks via generalized integral inequalities

This paper focuses on the synchronization problem of semi-Markovian jumping complex dynamical networks with time-varying coupling delays against actuator failures. In an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria. By constructing Lyapunov–Krasovski functional, some delay dependent criteria that assures the synchronization of CDN are derived with the help of the general integral inequalities. It should be noted that the general integral inequality used here is general than that of Jensen inequality, the Wirtinger-based inequality, the Bessel-Legendre inequality, the Wirtinger-based double integral inequality, and the auxiliary function-based integral inequalities. The resulting LMIs can be easily verified with the help of the available softwares. Finally, simulation results are proposed to verify the effectiveness of the general integral inequality and designed control law.     

Stability analysis for linear time-delay systems using new inequality based on the second-order derivative

This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.     

Observer design for semi-Markov jump systems with incremental quadratic constraints

This paper deals with the observer design problem for semi-Markov jump systems with incremental quadratic constraints. Based on the design objective that the state estimation error is stochastically stable, the sufficient conditions formulated by linear matrix inequalities are presented. To reduce the conservatism of sufficient conditions as well as the computational burden, the relaxation method with slack variable is employed. Finally, a simulation example verifies the effectiveness and superiority of the method studied in this paper.     

Synchronization control of neutral-type neural networks with sampled-data via adaptive event-triggered communication scheme

This paper addresses the problem of synchronization control of neutral-type neural networks with sampled-data, where sampled data will be over a communication network before received by controller. Generally, the communication network is with a bandwidth-limited communication channel. To reduce network burden, an event-triggered scheme is designed between the sampler and communication network. A weak synchronization conditions are derived by using our proposed integral inequality. Finally, a numerical example is given to illustrate the effectiveness and advantage of the proposed results.     

Interval approximation method for stability analysis of time-delay systems

This paper studies the stability analysis of linear systems with time-varying delay, which is supposed to be the trigonometric form. By utilizing the characteristics between time-varying delay and its derivative, a novel interval approximation method is proposed, which provides the new allowable delay sets. Then making use of Wirtinger inequality, reciprocally convex inequality and the looped Lyapunov–Krasovskii functionals, the stability criteria with less conservatism are obtained. Finally, two examples are used to show the effectiveness and efficiency of the stability criteria.     

Some augmented approaches to the improved stability criteria for linear systems with time-varying delays

This work investigates the improved stability conditions for linear systems with time-varying delays via various augmented approaches. Some augmented approaches are augmented Lyapunov-Krasovskii functionals, augmented zero equalities, and the augmented zero equality approach. At first, by constructing augmented Lyapunov-Krasovskii functionals including the state vectors which were not considered in the previous works and augmented zero equalities, a stability criterion is proposed in the forms of linear matrix inequalities. Through the proposed Lyapunov-Krasovskii functionals and an additional functional derived from the integral inequality, a slightly improved result is derived. The proposed results do not consider the increase in the computational complexity to achieve a larger delay bound. So, by applying the augmented zero equality approach, which is a method of grafting the proposed augmented zero equality proposed in Finsler Lemma, to the proposed result, an enhanced stability result was derived. Also, the computational complexity is reduced by appropriately adjusting any vector of the integral inequality utilized in the proposed criteria. By applying some numerical examples to the proposed conditions, the effectiveness and superiority of the results are confirmed.     

A delay-derivative-dependent approach to robust H∞ filter design for uncertain systems with time-varying distributed delays

This paper focuses on the problem of robust H∞ filter design for uncertain systems with time-varying state and distributed delays. System uncertainties are considered as norm-bounded time-varying parametric uncertainties. The delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A new delay-derivative-dependent approach of filter design for the systems is proposed. A novel Lyapunov-Krasovskii functional (LKF) is employed, and a tighter upper bound of its derivative is obtained by employing an inequality and using free-weighting matrices technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is established in terms of linear matrix inequality (LMI). Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed method.     

New fractional-order integral inequalities: Application to fractional-order systems with time-varying delay

In this paper, the problem of delay-dependent stability analysis of fractional-order systems with time-varying delay is investigated. First, a class of novel fractional-order integral inequalities for quadratic functions by constructing appropriate auxiliary functions is proposed, which has been proven to be useful in analyzing fractional-order systems with time-varying delay. Based on these proposed inequalities, the Lyapunov–Krasovskii functions are designed to deal with the time-varying delay terms, reducing the conservatism of the stability criteria. Furthermore, delay-dependent criteria are derived to achieve asymptotic stability of fractional-order systems with time-varying delay. Finally, two examples are provided to illustrate the effectiveness and feasibility of the proposed stability criteria.     

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H_∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H_∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H_∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.     

Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense

In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.     

Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality

This paper deals with the problem of delay-dependent stability analysis for neural networks with time-varying delays. First, by constructing an augmented Lyapunov–Krasovskii functional and utilizing a generalized free-weighting matrix integral inequality, an improved stability criterion for the concerned network is derived in terms of linear matrix inequalities. Second, by considering a marginal augmented vector and modifying a Lyapunov–Krasovsii functional, a further enhanced stability criterion is presented. Third, a less conservative stability condition in which a relaxed inequality related to activation functions is added is introduced. Finally, three numerical examples are included to illustrate the advantage and validity of the proposed criteria.     

Novel stability results for aperiodic sampled-data systems

This paper is concerned with stability for aperiodic sampled-data systems. Firstly, for aperiodic sampled-data systems without uncertainties, a new Lyapunov-like functional is constructed by introducing the double integral of the derivative of the state, the integral of the state, and the integral of the cross term of the state and the sampled state. When estimating the derivative of the Lyapunov-like functional, superior integral inequalities to Jensen inequality are employed to get a tighter upper bound. By the Lyapunov-like functional principle, sampling-interval-dependent stability results are derived. Then, the stability results are extended to aperiodic sampled-data systems with polytopic uncertainties. Finally, some examples are listed to show the stability results have less conservatism than some existing ones.     

New absolute stability criteria for uncertain Lur’e systems with time-varying delays

This paper deals with absolute stability of uncertain Lur’e systems with time-varying delay. By introducing a Lyapunov–Krasovskii functional related to a second-order Bessel–Legendre inequality, some absolute stability criteria are derived for the system under study. Different from some existing approaches, a remarkable feature of this paper is that the time-derivative of the Lyapunov–Krasovskii functional is estimated by a linear function rather than a quadratic function on the time-varying delay, thanks to the introduction of four extra vectors. As a result, the resulting absolute stability criteria are of less conservatism than some existing ones, which is demonstrated through three examples.     

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.