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1.
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   

2.
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   

3.
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   

4.
This paper is concerned with the problem of global finite-time stabilization via output feedback for a class of switched stochastic nonlinear systems whose powers are dependent of the switching signal. The drift and diffusion terms satisfy the lower-triangular homogeneous growth condition. Based on adding a power integrator technique and the homogeneous domination idea, output-feedback controllers of all subsystems are constructed to achieve finite-time stability in probability of the closed-loop system. Distinct from the existing results on switched stochastic nonlinear systems, the delicate change of coordinates are introduced for dominating nonlinearities. Moreover, by incorporating a multiplicative design parameter into the coordinate transformations, the obtained control method can be extended to switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition. The validity of the proposed control methods is demonstrated through two examples.  相似文献   

5.
In this paper, finite-time stabilization of switched linear systems with saturating actuators is discussed by virtue of time domain approach. State feedback controllers are designed to make the closed-loop systems finite-time stable. If the state is unavailable, observer-controller compensators are used. The results not only give sufficient conditions for finite-time stabilization of switched linear systems with saturating actuator, but also show the effect of the switching signals on finite-time stabilization of the system. Moreover, based on average dwell-time technique, we present the average dwell-time of switching signals to guarantee finite-time stability of the closed loop system. An example is employed to verify the efficiency of the proposed method.  相似文献   

6.
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   

7.
Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.  相似文献   

8.
The paper is concerned with the stability and stabilization problems for a family of hybrid linear parameter-varying systems with stochastic mode switching. The switching phenomenon is modeled by a semi-Markov stochastic process which is more generalized than a Markov stochastic process. With the construction of a Lyapunov function that depends on both the parameter variation and operating mode, numerical testable stability and stabilization criteria are established in the sense of σ-error mean square stability with the aid of some mathematical techniques that can eliminate the terms containing products of matrices. To test the effectiveness of the designed stabilizing controller, we apply the developed theoretical results to a numerical example.  相似文献   

9.
This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method.  相似文献   

10.
《Journal of The Franklin Institute》2019,356(18):11520-11545
This paper focuses on the stability analysis and stabilization problem for a class of uncertain switched delay systems with Lévy noise and flexible switching signals which unify the high-frequency switching and low-frequency switching. By employing the theory of switched systems, mathematical induction and stochastic analysis technique, some sufficient conditions in form of algebraic inequalities are derived to guarantee the stability and stabilization of such systems. Different from dwell time and average dwell time, the proposed switching rule constrained the partial dwell-time shows that the switching number in the same time interval can be more elastic. Finally, numerical examples are implemented to illustrate the effectiveness of the theoretical results.  相似文献   

11.
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   

12.
The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach.  相似文献   

13.
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   

14.
In this paper, the finite-time stability and asynchronous resilient control for a class of Itô stochastic semi-Markov jump systems are studied. Firstly, the sufficient conditions of the finite-time stability for stochastic semi-Markovian jump systems are given. Secondly, the state feedback and observer-based finite-time asynchronous resilient controllers are designed. By multiple Lyapunov functions approach, the sufficient conditions for the existence of these two types of controllers which make the system stochastically stabilizable in finite time are given. Compared with nonresilient case, the existence of the resilient controller can eliminate the influence of the uncertainties and get better results. Finally, a numerical example is given to verify the effectiveness of our results.  相似文献   

15.
This paper deals with the input–output finite-time stabilization problem for Markovian jump systems (MJSs) with incompletely known transition rates. An observer-based output feedback controller is constructed to study the input–output finite-time stability (IO-FTS) problem. By using the mode-dependent Lyapunov–krasovskii functional method, a sufficient criterion checking the IO-FTS problem is provided. Then, an observer and a corresponding state feedback controller for the individual subsystem are respectively designed to solve the input–output finite-time stabilization problem for the systems. Finally, a numerical example on the mass-spring system model is investigated to bring out the advantages of the control scheme proposed in this paper.  相似文献   

16.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty. Finally, we present two numerical examples for finite-time stabilization involving a large-scale dynamical system and a combustion control system.  相似文献   

17.
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   

18.
In this article, the finite-time stability problem is investigated for a kind of stochastic nonlinear systems subject to asymmetric output constraints. Firstly, a new asymmetric barrier Lyapunov function (BLF) is introduced to deal with the constraint on output variable. Further, through incorporating the proposed BLF into the adding a power integrator technique, a state-feedback controller is explicitly designed. With the help of the stochastic Lyapunov stability theory, it is then proved that the origins of the considered systems are finite-time stable in probability under the designed controller. Meanwhile, the proposed control scheme also guarantees that the pre-given output constraint is not violated in the almost sure sense. Finally, the simulation results of an example are provided to demonstrate the derived theoretical conclusion.  相似文献   

19.
This paper investigates the finite-time stability (FTS) and finite-time stabilization for a class of nonlinear singular time-delay Hamiltonian systems, and proposes a number of new results on these issues. Firstly, an equivalent form is obtained for the nonlinear singular time-delay Hamiltonian systems by the singular matrix decomposition method, based on which some delay-independent and delay-dependent conditions on the FTS are derived for the systems by constructing a kind of novel Lyapunov function. Secondly, we use the equivalent form as well as the energy shaping plus damping injection technique to investigate the finite-time stabilization problem for a class of nonlinear singular port-controlled Hamiltonian (PCH) systems with time delay, and present a specific control design procedure for the systems. Finally, we give several illustrative examples to show the effectiveness of the results obtained in this paper.  相似文献   

20.
This paper is devoted to the adaptive finite-time control for a class of stochastic nonlinear systems driven by the noise of covariance. The traditional growth conditions assumed on the drift and diffusion terms are removed through a technical lemma, and the negative effect generated by unknown covariance noise is compensated by combining adaptive control technique with backstepping recursive design. Then, without imposing any growth assumptions, a smooth adaptive state-feedback controller is skillfully designed and analyzed with the help of the adding a power integrator method and stochastic backstepping technique. Distinctive from the global stability in probability or asymptotic stability in probability obtained in related work, the proposed design algorithm can guarantee the solution of the closed-loop system to be finite-time stable in probability. Finally, a stochastic simple pendulum system is skillfully constructed to demonstrate the effectiveness of the proposed control scheme.  相似文献   

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