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1.
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
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.  相似文献   

8.
This paper focuses on the stability analysis of systems with interval time-varying delay. A new augmented vector containing single and double integral terms is constructed and the corresponding Lyapunov functional with triple integral terms is introduced. In order to improve the estimating accuracy of the derivatives of the constructed Lyapunov functional, single integral inequalities and double integral inequalities via auxiliary functions are employed on the first step, then an extended relaxed integral inequality and reciprocally convex approach are further utilized to narrow the scaling room of the functional derivatives. As a result, some novel delay-dependent stability criteria with less conservatism are derived. Finally, numerical examples are provided to check the effectiveness of the theoretical results and the improvement of the proposed method over the existing works.  相似文献   

9.
This paper considers a stability analysis problem for continuous-time Markovian jump linear systems under aperiodic samplings which are represented as Markovian jump linear systems with input delay. For the systems, this paper constructs a Lyapunov functional by utilizing a fragmented-delay state, which is defined between the last sampling instant and the present time, and a new state space model of the fragmented state. Based on the Lyapunov functional, a stability criterion is derived in terms of linear matrix inequalities by using reciprocally convex approach and integral inequality. Here, the reciprocally convex approach and integral inequality are associated not only with the current state, the delayed state, and the maximum-admissible delay state, but also with the fragmented-delay state. The simulation result shows the effectiveness of the proposed stability criterion.  相似文献   

10.
This paper studies the stochastic stability and extended dissipativity analysis for delayed Markovian jump neural networks (MJNNs) with partly unknown transition rates (PUTRs) using novel integral inequality. A new double integral inequality with augmented vector is introduced through inequality technique and the zero-valued equality approach, which can more efficiently estimate the derivative of the triple integral inequality. Next, an augmented Lyapunov-Krasovskii functional (LKF) with delay-product-type (DPT) is constructed. Besides, with the introduced integral inequality, the augmented LKF and some other analytical techniques, some less conservative extended dissipation conditions are obtained in the form of linear matrix inequality (LMI). Finally, several examples are provided to illustrate the effectiveness of the obtained results.  相似文献   

11.
This paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated.  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
This paper presents a new stability analysis of networked control systems (NCSs) with network-induced delay and packet dropout. A novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which takes into account the feature of the sawtooth delay induced by sample-and-hold. Based on an improved version of Wirtinger's inequality and the convex combination method, a delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The advantage of the proposed criterion lies in its simplicity and less conservativeness than some of the existing results. The new criterion is applied to the network-based state feedback control problems. Numerical examples are given to verify the effectiveness of the proposed criterion.  相似文献   

17.
This paper is concerned with the problem of exponentially extended dissipative criteria for a class of delayed discrete-time neural networks (DNNs) subject to resilient observer-based controller design. For this objective, a memoryless full-order Luenberger state observer is designed, and further, its observer error system is calculated with resilient control. Initially, some new improved weighted summation inequalities are proposed by combining weighted summation inequality and an extended reciprocal convex matrix inequality. By constructing the suitable Lyapunov-Krasovskii functional (LKF) and utilizing the developed summation inequalities, the exponentially extended dissipative criterion is obtained for the considered delayed DNNs. The designed observer and resilient control gain matrices can be determined by solving a set of linear matrix inequalities (LMIs) subject to the prescribed exponential decay rate. Finally, two numerical examples are carried out to illustrate the feasibility and effectiveness of the established theoretical results obtained through the newly developed summation inequalities.  相似文献   

18.
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.  相似文献   

19.
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.  相似文献   

20.
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.  相似文献   

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