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 共查询到20条相似文献，搜索用时 31 毫秒
1.
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   

2.
This paper is concerned with the stability analysis of time-varying delay systems. Unlike the construction of augmented Lyapunov functional and multiple integral Lyapunov functional, novel three Lyapunov functionals are suggested which are delay product type functions and lead to less conservative results. Based on newly developed Lyapunov functionals, three stability criteria are derived and their superiority is described by three numerical examples.  相似文献   

3.
This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.  相似文献   

4.
This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.  相似文献   

5.
This paper is concerned with the stability of sampled-data systems with constant delay. Firstly, by dividing the interval of sampling periods in two subintervals, two separate looped functionals are employed in each of these subintervals. Then, a new Lyapunov functional that combines classical Lyapunov functionals and looped-functionals is constructed. Furthermore, several zero equalities which consider the intrinsic relationships of state vectors in the system are introduced into the derivative of the constructed functional, and some stability criteria with less conservatism are obtained in forms of linear matrix inequalities (LMIs). Finally, two numerical examples are carried out as to verify the effectiveness and advantages of our method.  相似文献   

6.
In this paper, the stability problem of discrete-time systems with time-varying delay is considered. Some new stability criteria are derived by using a switching technique. Compared with the Lyapunov–Krasovskii functional (LKF) approach, the method used in this paper has two features. First, a switched model, which is equivalent to the original system and contains more delay information, is introduced. It means that the criteria obtained by using the LKF method can be regarded as stability criteria for the switched system under arbitrary switching. Second, when the switching signal is known, the stability problem for the switched model under constrained switching is considered and piecewise LKFs are adopted to obtain stability criteria. Since constrained switching is less conservative than arbitrary switching if the switching signal is known, one can know that the obtained results in this paper are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the obtained results.  相似文献   

7.
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   

8.
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.  相似文献   

9.
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.  相似文献   

10.
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.  相似文献   

11.
This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.  相似文献   

12.
The problem of robust finite-time stability (RFTS) for singular nonlinear systems with interval time-varying delay is studied in this paper. Some delay-dependent sufficient conditions of RFTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii functional (LKF) method and singular analysis technique. Two examples are provided to show the applications of the proposed criteria.  相似文献   

13.
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.  相似文献   

14.
This paper investigates the problem of decentralized adaptive backstepping control for a class of large-scale stochastic nonlinear time-delay systems with asymmetric saturation actuators and output constraints. Firstly, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are designed to ensure that the output parameters are restricted. Secondly, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. At last, based on Lyapunov stability theory, a decentralized adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters. It is shown that the designed controller can ensure that all the closed-loop signals are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are provided to show the effectiveness of the proposed method.  相似文献   

15.
In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.  相似文献   

16.
The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.  相似文献   

17.
The problem of existence of almost periodic solutions of uncertain impulsive functional differential systems of fractional order is investigated. Using the Lyapunov method combined with the concept of uniformly positive definite matrix functions and Hamilton–Jacobi–Riccati inequalities new criteria are presented. The robust stability of the almost periodic solution is also discussed. We apply our results to an impulsive Lasota–Wazewska type model of fractional order. Our results extend the theory of almost periodic solutions for impulsive delay differential equations to the fractional-order case under uncertainty.  相似文献   

18.
The present article is concerned with the fixed-time stability(FxTS) analysis of the nonlinear dynamical systems with impulsive effects. The novel criteria have been derived to achieve stability of the non-autonomous dynamical system in fixed-time under the effects of stabilizing and destabilizing impulses. The fixed time stability analysis due to the presence of destabilizing impulses in dynamical system, that leads to behavior of perturbing the systems’ stability, have not been addressed much in the existing literature. Therefore, two theorems are constructed here, for stabilizing and destabilizing impulses separately, to estimate the fixed-time convergence precisely by using the concept of Lyapunov functional and average impulsive interval. The theoretical derivation shows that the estimated fixed-time in this study is less conservative and more accurate as compared to the existing FxTS theorems. Further, the theoretical results are applied to the impulsive control of general neural network systems. Finally, two numerical examples are given to validate the effectiveness of the theoretical results.  相似文献   

19.
The paper is a study of quantized control for stochastic Markov jump systems with interval time-varying delays and bounded system noise under event-triggered mechanism. A new scheme of Lyapunov–Krasovskii functional which contains the quadratic terms and integral terms is presented. Then quadratic convex technology, the theory of stochastic switching system, and logarithmic quantizer are applied to this paper. The design of quantized controller is obtained with those methodologies. Different from previous results, our derivation applies the idea of second-order convex combination. The conservatism of stability criteria for systems is reduced by using this method. A numerical example under different conditions is given to demonstrate the effectiveness and validity of the new design techniques.  相似文献   

20.
This paper studies bounded input bounded output (BIBO) stability for a class of neutral systems with time-varying delays. Based on Lyapunov method and linear matrix inequalities, some new BIBO stability criteria are established. The numerical simulation is made to demonstrate the effectiveness of the theoretical results obtained in this paper.  相似文献   

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