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1.
This paper is concerned with the finite-time stability, boundedness and H∞ control problems for a class of switched stochastic systems. Using the average dwell time method and the multiple Lyapunov-like function technique, some sufficient conditions are proposed to guarantee the finite-time properties for the switched stochastic systems in the form of matrix inequalities. Also, a state feedback controller for the finite-time H∞ control problem is obtained. An example is employed to verify the effectiveness of the proposed method.  相似文献   

2.
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   

3.
The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.  相似文献   

4.
This paper is concerned with the finite-time stabilization for a class of stochastic BAM neural networks with parameter uncertainties. Compared with the previous references, a continuous stabilizator is designed for stabilizing the states of stochastic BAM neural networks in finite time. Based on the finite-time stability theorem of stochastic nonlinear systems, several sufficient conditions are proposed for guaranteeing the finite-time stability of the controlled neural networks in probability. Meanwhile, the gains of the finite-time controller could be designed by solving some linear matrix inequalities. Furthermore, for the stochastic BAM neural networks with uncertain parameters, the problem of robust finite-time stabilization could also be ensured as well. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.  相似文献   

5.
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.  相似文献   

6.
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.  相似文献   

7.
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   

8.
This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.  相似文献   

9.
In this paper, we deal with the finite-time stability of positive switched linear time-delay systems. By constructing a class of linear time-varying copositive Lyapunov functionals, we present new explicit criteria in terms of solvable linear inequalities for the finite-time stability of positive switched linear time-delay systems under arbitrary switching and average dwell-time switching. As an important application, we apply the method to finite-time stability of linear time-varying systems with time delay.  相似文献   

10.
This paper is concerned with the issue of finite-time boundedness of discrete-time uncertain interval type-2 fuzzy systems with time-varying delay and external disturbances via an observer-based reliable control strategy. According to the system output variable, a full-state observer that shares the same membership functions of the plant is constructed to estimate the unknown system states. In addition, a reliable controller subject to observer states and actuator faults is designed to formulate the closed-loop feedback control system, which does not share the same membership functions of the plant. Then, by constructing an appropriate Lyapunov–Krasovskii functional and using the finite-time stability theory, a new set of delay-dependent sufficient conditions guaranteeing the finite-time boundedness of the addressed system is established in the framework of linear matrix inequalities. Furthermore, the explicit expressions of gain matrices of the state observer and the reliable controller are given in terms of the established sufficient conditions. Finally, simulation results are presented to demonstrate the effectiveness of the obtained theoretical results.  相似文献   

11.
This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods.  相似文献   

12.
In this paper, we provide an efficient approach based on combination of singular value decomposition (SVD) and Lyapunov function methods to finite-time stability of linear singular large-scale complex systems with interconnected delays. By representing the singular large-scale system as a differential-algebraic system and using Lyapunov function technique, we provide new delay-dependent conditions for the system to be regular, impulse-free and robustly finite-time stable. The conditions are presented in the form of a feasibility problem involving linear matrix inequalities (LMIs). Finally, a numerical example is presented to show the validity of the proposed results.  相似文献   

13.
This paper pays attention to the finite-time stability problem for the singular system with time delay. Some improved inequalities are presented and by employing these inequalities along with the Lyapunov-Krasovskii functional method, an improved sufficient condition which ensures that the investigated system is regular, impulse-free and finite-time stable is derived. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed approach.  相似文献   

14.
This paper focuses on the issue of finite-time stability for a general form of nonlinear systems subject to state-dependent delayed impulsive controller. Based on the Lyapunov theory and the impulsive control theory, sufficient conditions for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained. Additionally, we apply theoretical results to finite-time synchronization of chaotic systems and design the effective state-dependent delayed impulsive controllers in terms of techniques of linear matrix inequality (LMI). Finally, we present two numerical examples of finite-time synchronization of cellular neural networks and Chua’s circuit to verify the effectiveness of our results.  相似文献   

15.
This paper improves stability criteria for neutral-type Lur’e systems with time-varying delays, where the nonlinearity satisfies sector and slope restrictions. A proposed Lyapunov–Krasovskii functional consisting of a quadratic term and integral terms for the time-varying delays and the nonlinearities, has four different characteristics. First, the quadratic term utilizes not only the current and delayed states but also the nonlinear vectors. Second, the integral terms for nonlinearities fully exploit the characteristics of sector and slope restrictions. Third, the integral terms for nonlinearities also exploit the characteristic of incremental restriction induced from the slope restriction. Fourth, this paper utilizes a vector related to the time derivative of the neutral delayed state to handle the neutral delay. Based on the proposed Lyapunov–Krasovskii functional, the improved stability criteria are derived in terms of linear matrix inequalities. Numerical examples show that the proposed criteria present less conservative results than the previous criteria.  相似文献   

16.
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   

17.
The paper is concerned with the finite-time fault detection (FTFD) problem for a class of delayed networked systems subject to conic-type nonlinearity and randomly occurring deception attacks (RODAs) via dynamic event-triggered mechanism (DETM). The nonlinear function with the conic-type constraint is limited to a known hypersphere with uncertain center. Moreover, a variable governed by Bernoulli distribution is introduced to characterize the RODAs phenomenon. In order to reduce unnecessary communication transmissions, a DETM is considered in the design of finite-time fault detection filter (FTFDF) for the addressed networked systems with time-delays. This paper focuses on the design of an FTFDF via the DETM to ensure the finite-time stochastic stability of error dynamics system with satisfactory the prescribed H∞ performance. Moreover, the desired FTFDF parameter matrices are obtained by solving linear matrix inequalities. In the end, a simulation example is employed to illustrate the validity of the proposed FTFD method.  相似文献   

18.
The primary goal of this paper is to examine the finite-time stability and finite-time contractive stability of the linear systems in fractional domain with time-varying delays. We develop some sufficient criteria for finite-time contractive stability and finite-time stability utilizing fractional-order Lyapunov-Razumikhin technique. To validate the proposed conditions, two different types of dynamical systems are taken into account, one is general time-delay fractional-order system and another one is fractional-order linear time-varying time-delay system, furthermore the efficacy of the stability conditions is demonstrated numerically.  相似文献   

19.
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   

20.
In this paper, we investigate the problem of finite-time stabilization of time-varying delayed neural networks with uncertainty. By employing the Lyapunov approach and linear matrix inequalities (LMIs), two different memory controllers are derived to achieve the finite-time stabilization of the addressed neural networks. Moreover, the upper bound of the setting-time for stabilization can be estimated via different Lyapunov functions. Our results improve and extend some recent works. Finally, the effectiveness and feasibility of the proposed controllers are demonstrated by numerical simulations.  相似文献   

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