共查询到20条相似文献,搜索用时 46 毫秒
1.
讨论随机系统的有限时间镇定问题.首先提出了随机系统有限时间稳定的概念;其次证明了随机系统有限时间稳定的Lyapunov定理;然后,讨论了一类随机系统的镇定问题. 相似文献
2.
Observer-based finite-time control of time-delayed jump systems 总被引:1,自引:0,他引:1
This paper provides the observer-based finite-time control problem of time-delayed Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time H∞ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches. 相似文献
3.
This paper studies the robust and resilient finite-time H∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples. 相似文献
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This paper is devoted to investigating the problem of robust sliding mode control for a class of uncertain Markovian jump linear time-delay systems with generally uncertain transition rates (GUTRs). In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. A sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates. Finally, an example is presented to verify the validity of the proposed method. 相似文献
6.
In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods. 相似文献
7.
Positive results are derived concerning the long time dynamics of fixed step size numerical simulations of stochastic differential
equation systems with Markovian switching. Euler–Maruyama and implicit theta-method discretisations are shown to capture exponential
mean-square stability for all sufficiently small time-steps under appropriate conditions. Moreover, the decay rate, as measured
by the second moment Lyapunov exponent, can be reproduced arbitrarily accurately. New finite-time convergence results are
derived as an intermediate step in this analysis. We also show, however, that the mean-square A-stability of the theta method
does not carry through to this switching scenario. The proof techniques are quite general and hence have the potential to
be applied to other numerical methods. 相似文献
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9.
Yingqi Zhang 《Applied mathematics and computation》2012,218(9):5629-5640
This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology. 相似文献
10.
Stability in distribution of stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems. There are several papers which study this stability for stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching technically. In our paper, we are concerned with the general neutral stochastic functional differential equations with Markovian switching and we derive the sufficient conditions for stability in distribution. At the end of our paper, one example is established to illustrate the theory of our work. 相似文献
11.
In this paper, the finite-time synchronization and identification for the uncertain system parameters and topological structure of complex delayed networks with Markovian jumping parameters and stochastic perturbations is studied. On the strength of finite time stability theorem and appropriate stochastic Lyapunov–Krasovskii functional under the Itô’s formula, some sufficient conditions are obtained to assurance that the complex delayed networks with Markovian switching dynamic behavior can be identified the uncertain parameters and topological structure matrix in finite time under stochastic perturbations. In addition, three numerical simulations of different situation and dimension are presented to illustrate the effectiveness and feasibility of the theoretical results. 相似文献
12.
p-Moment Stability of Stochastic Nonlinear Delay Systems with Impulsive Jump and Markovian Switching
Zaiming Liu 《随机分析与应用》2013,31(5):911-923
Abstract This article is concerned with the problem of p-moment stability of stochastic differential delay equations with impulsive jump and Markovian switching. In this model, the features of stochastic systems, delay systems, impulsive systems, and Markovian switching are all taken into account, which is scarce in the literature. Based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain new criteria ensuring p-moment stability of trivial solution of a class of impulsive stochastic differential delay equations with Markovian switching. 相似文献
13.
This works is concerned with the finite-time optimal stabilization problem for a class of switched non-strict-feedback nonlinear systems whose powers are possibly different positive odd rational numbers in the sense the powers of each subsystem might differ from others. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping method successfully developed for low-order systems fail to work. To this purpose, the nested saturation homogeneous controller is constructively devised to achieve global finite-time stability. Furthermore, the corresponding design parameters are optimized by minimizing a well-defined cost function, and thus an optimal controller being independent of switching signals is obtained. Simulation results are eventually provided to validate the effectiveness of the proposed control scheme. 相似文献
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In this paper, problems of stability and optimal control for a class of stochastic singular systems are studied. Firstly, under some appropriate assumptions, some new results about mean-square admissibility are developed and the corresponding LMI sufficient condition is given. Secondly, finite-time horizon and infinite-time horizon linear quadratic (LQ) control problems for the stochastic singular system are investigated, in which the coefficients are allowed to be random in control input and quadratic criterion. Some results involving new stochastic generalized Riccati equation are discussed as well. Finally, the proposed LQ control model for stochastic singular systems provides an appropriate and effective framework to study the portfolio selection problem in light of the recent development on general stochastic LQ problems. 相似文献
16.
Zhengrong Xiang Ronghao WangQingwei Chen 《Applied mathematics and computation》2011,217(19):7725-7736
This paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system. A design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures, and the dwell time approach is utilized for the stability analysis. Then the approach is extended to take into account stochastic switched system with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is employed to verify the proposed method. 相似文献
17.
This work studies stability and stochastic stabilization of numerical solutions of a class of regime-switching jump diffusion systems. These systems have a wide range of applications in communication systems, flexible manufacturing and production planning, financial engineering and economics because they involve three classes of stochastic factors: white noise, Poisson jump and Markovian switching. This paper focuses on the stability of numerical solutions of the switching jump diffusion systems and examines the conditions under which the Euler–Maruyama (EM) and the backward EM may share the stability of the exact solution. These conditions show that all these three classes of stochastic factors may serve as stabilizing factors and play positive roles for the stability property of both exact and numerical solutions. 相似文献
18.
Xuerong Mao James Lam Huijun Gao 《Journal of Mathematical Analysis and Applications》2006,314(1):45-66
This paper deals with the exponential stability of hybrid stochastic delay interval systems (also known as stochastic delay interval systems with Markovian switching). The known results in this area (see, e.g., [X., Mao, Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Automat. Control 47 (10) (2002) 1604-1612]) require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics. The main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only. The Razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay. 相似文献
19.
Fenglan Sun Jiancong Chen Zhi-Hong Guan Li Ding Tao Li 《Nonlinear Analysis: Real World Applications》2012,13(5):2271-2284
Finite-time consensus problems of the leader-following multi-agent systems with jointly-reachable leader and switching jointly-reachable leader are studied in this paper. Based on the graph theory, LaSalle’s invariance principle and Lyapunov stability theory, the finite-time consensus protocols are presented for the first-order and second-order leader-following systems. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results. 相似文献