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1.
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   

2.
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   

3.
In this paper, the problem of delay-dependent stability of a class of uncertain Lur’e systems of neutral type with interval time-varying state delay and sector-bounded nonlinearity has been considered based on Lyapunov–Krasovskii functional approach. By constructing a candidate Lyapunov–Krasovskii (LK) functional, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs). The reduction in conservatism of the proposed stability criteria over recently reported results is attributed to the candidate LK functional used in the delay-dependent stability analysis, and to the tighter bounding of the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability condition in convex LMI framework, and is solved non-conservatively at boundary conditions using standard numerical packages. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.  相似文献   

4.
This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler’s lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples.  相似文献   

5.
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   

6.
《Journal of The Franklin Institute》2019,356(18):11561-11580
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.  相似文献   

7.
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   

8.
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   

9.
《Journal of The Franklin Institute》2023,360(14):10815-10835
  相似文献   

10.
In this paper, the problem of synchronization on interval type-2 (IT2) stochastic fuzzy complex dynamical networks (CDNs) with time-varying delay via fuzzy pinning control is fully studied. Firstly, a more general complex network model is considered, which involves the time-varying delay, IT2 fuzzy and stochastic effects. More specifically, IT2 fuzzy model, as a meaningful fuzzy scheme, is investigated for the first time in CDNs. Then, with the aid of Lyapunov stability theory and stochastic analysis technique, some new sufficient criteria are established to ensure synchronization of the addressed systems. Moreover, on basis of the parallel-distributed compensation (PDC) scheme, two effective fuzzy pinning control protocols are proposed to achieve the synchronization. Finally, a numerical example is performed to illustrate the effectiveness and superiority of the derived theoretical results.  相似文献   

11.
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   

12.
This paper investigates the problems of stochastic admissibility and extended dissipativity analysis as well as state feedback controller design for interval type-2 singular systems with nonhomogeneous Markovian switching. By utilizing matrix decomposition technique to deal with the time-dependent transition rates, a sufficient condition is established to guarantee that the systems under consideration are regular, impulse-free, stochastically asymptotically stable and extended dissipative. For developing the state feedback controller in light of the obtained sufficient condition, a novel lemma is proposed inspired by Projection lemma, based on which an approach of controller design is provided. It should be pointed out that no conservatism is introduced in controller design due to the sufficiency and necessity of this lemma. Finally, simulation examples are provided to show the effectiveness of the proposed approach.  相似文献   

13.
This paper addresses the new stability analysis method for systems with interval time-varying delay. By taking single-integral and double-integral terms with time-varying bound into consideration, a new Lyapunov–Krasovskii functional is defined. Then reciprocally convex approach and some transformations are used to estimate the derivative of the constructed functional less conservatively, and as a result, some new stability criteria are obtained in terms of the quadratic convex combination, which are less conservative and have less decision variables. Two well-known examples are also given to illustrate the advantage of the main results.  相似文献   

14.
This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.  相似文献   

15.
This paper is devoted to investigating the robust stochastic exponential stability for reaction-diffusion Cohen–Grossberg neural networks (RDCGNNs) with Markovian jumping parameters and mixed delays. The parameter uncertainties are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Some criteria for delay-dependent robust exponential stability of RDCGNNs with Markovian jumping parameters are established in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing Matlab LMI toolbox. Numerical examples are provided to demonstrate the efficiency of the proposed results.  相似文献   

16.
In this paper, the dissipativity-based dynamic output feedback controller (DOFC) design for Semi-Markovian jump systems under stochastic cyber-attacks is first proposed. It is assumed that the time-varying uncertainties obey Bernoulli-distribution and transition probability matrix is time-varying and partially accessed. By utilizing the dissipativity-based technique, sufficient conditions for the existence of the DOFC are obtained to ensure the exponential stability with a strict dissipative performance of the resulted system. Next, the proposed results are improved by fractionalizing the time-varying transition probability matrix and the corresponding DOFC gains are obtained by cone complementarity linearization algorithm. Simulations results are provided to demonstrate the effectiveness and theoretical value of the proposed dissipativity-based DOFC design method.  相似文献   

17.
《Journal of The Franklin Institute》2022,359(18):10355-10391
In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.  相似文献   

18.
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   

19.
This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.  相似文献   

20.
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.  相似文献   

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