分数阶微分中立型系统的有限时间镇定性及有界性

讨论了一类分数阶微分中立型系统的有限时间状态反馈镇定性及有界性问题.利用Gronwall 不等式, 获得了使得系统有限时间状态反馈镇定及有限时间有界的充分性条件.     

分数阶微分中立型系统的有限时间镇定性及有界性（英文）

讨论了一类分数阶微分中立型系统的有限时间状态反馈镇定性及有界性问题.利用Gronwall不等式,获得了使得系统有限时间状态反馈镇定及有限时间有界的充分性条件.     

一类具有零动态不确定非线性系统的有限时间镇定问题

研究了一类带有零动态不确定非线性系统的有限时间镇定问题.基于有限时间稳定的Lyapunov理论和反推技术给出了一个状态反馈控制器的设计步骤,解决了这类不确定非线性系统的有限时间镇定问题.     

一类随机非线性系统的全局有限时间状态反馈镇定

研究一类连续但非光滑的随机非线性系统的全局有限时间状态反馈镇定控制问题.通过增加幂次积分器技术和四次Lyapunov函数的构造,系统地给出了系统状态反馈有限时间镇定控制器的设计方法.基于引入的随机非线性系统有限时间稳定的判定准则,可以证明闭环系统的有限时间稳定性.仿真结果进一步验证了所设计控制器的有效性.     

一类非自治随机时滞系统的状态反馈镇定

本文讨论一类非自治随机时滞系统的状态反馈镇定问题.一方面,考虑到模型的特征(复杂非线性、随机以及非自治),本文在反步框架下设计随机时滞系统的时变反馈控制器,给出相应的状态反馈控制策略;另一方面,基于随机Razumikhin稳定性理论来分析系统的依概率全局渐近稳定性,放宽了系统镇定对时滞项的要求.最后,利用数值仿真验证了反馈控制器及控制策略的有效性.     

自治非光滑时滞系统的有限时间稳定

主要讨论右端非光滑的自治时滞系统在Filippov解意义下的有限时间稳定问题.基于Filippov微分包含和非光滑的Lyapunov-Krasovskii泛函,提出自治非光滑时滞系统有限时间稳定的定义和比较原理,并给出有限时间稳定的Lyapunov定理.     

差分包含的有限时间稳定

主要讨论差分包含系统的有限时间稳定问题,基于集值映射和Lyapunov函数给出差分包含的有限时间稳定性的充分条件.     

随机系统的Peuteman-Aeyels指数稳定性定理

把Peuteman-Aeyels指数稳定性定理从确定性系统推广到随机系统.并借此讨论了随机混杂系统的均方指数镇定问题,得出了系统在同步切换下可镇定的充分必要条件.     

分段脉冲系统的有限时间稳定与滤波

利用线性矩阵不等式和松弛变量方法,研究连续时间分段脉冲系统的有限时间稳定和滤波问题.一方面给出滤波误差系统有限时间稳定和满足性能要求的充分条件.另一方面给出有限时间滤波问题可解的充分条件和滤波器的设计方法.最后通过数值算例表明结论的可行性和有效性.     

网络化非周期采样控制系统的主动时间滞后控制:随机脉冲切换系统方法

研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响,并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统,...     

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.     

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

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.     

Observer-based finite-time control of time-delayed jump systems

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.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

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.     

Global finite-time stabilization of switched high-order rational power nonlinear systems

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.     

不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.     

Adaptive Stabilization of Nonlinear Stochastic Systems

The purpose of this paper is to study the problem of asymptotic stabilization in probability of nonlinear stochastic differential systems with unknown parameters. With this aim, we introduce the concept of an adaptive control Lyapunov function for stochastic systems and we use the stochastic version of Artstein's theorem to design an adaptive stabilizer. In this framework the problem of adaptive stabilization of a nonlinear stochastic system is reduced to the problem of asymptotic stabilization in probability of a modified system. The design of an adaptive control Lyapunov function is illustrated by the example of adaptively quadratically stabilizable in probability stochastic differential systems. Accepted 9 December 1996     

Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

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.     

Global stability and stabilization of more general stochastic nonlinear systems

This paper considers the global stability and stabilization of more general stochastic nonlinear systems. Due to the absence of the conventional assumptions (e.g., Lipschitz condition), the stochastic nonlinear systems under investigation may have more than one weak solution. However, the most associated results are only applicable to the stochastic systems having a unique strong solution, and therefore, it is meaningful to refine and extend the relevant concepts and methods to the more general case. In this paper, the concepts of stochastic stability in the more general sense are first introduced to cover the stochastic nonlinear systems having more than one weak solution. Then, the generalized stochastic Barbashin–Krasovskii theorem and LaSalle theorem are established, which present the criterions of stochastic stability for more general stochastic nonlinear systems. As one of the main contributions in this paper, we rigorously prove the generalized stochastic Barbashin–Krasovskii theorem. Moreover, based on the generalized theorems, the output-feedback and state-feedback stabilization are accomplished respectively for two classes of high-order stochastic nonlinear systems under rather weaker assumptions comparing to the existing literature.     

Global finite-time stabilization of a class of nonlinear system based on a dynamic gain approach

In this paper, finite-time control problem of a class of nonlinear systems is considered. By using a dynamic gain-based backstepping approach, a state feedback controller involving the dynamic gains is constructed with the help of appropriate Lyapunov function, which guarantees the closed-loop system to be globally finite-time stabilization. A simulation example is provided to illustrate the effectiveness of the proposed control scheme.