时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

仿射切换系统的有限时间鲁棒??∞ 跟踪控制

针对一类含分段常数项的仿射切换系统,在平均滞留时间分析方法的基础上研究此类系统的有限时间有界性(FTB)和干扰抑制问题。给出了仿射切换系统的FTB概念以及有限时间鲁棒??∞性能的定义,并在此基础上提出使得系统有限时间内有界的充分条件以及??∞控制器的设计方法,所得结论均以线性矩阵不等式(LMI)的形式给出。最后通过算例验证了所提出方法的正确性和有效性。     

基于有限时间的一类时滞非线性切换系统滑模控制

研究一类时滞非线性切换系统的有限时间滑模控制问题.针对所研究的系统模型,构造每个子系统对应的积分滑模面,基于滑模控制理论,设计带有状态时滞的滑模控制器使得每个子系统能在有限时间内到达相应的滑模面上,并对系统中存在的非线性项采用Lipschitz条件进行处理.根据多李亚普诺夫函数、平均驻留时间方法以及分割策略引理,给出滑模趋近段和滑模动态有限时间有界的充分条件,并通过对线性矩阵不等式的求解得到控制器增益.最后,通过一个数值仿真例子验证该设计方法的有效性.     

不确定时变时滞模糊系统的有限时间H∞滤波

研究了一类复杂非线性系统的有限时间H∞滤波问题.针对由Takagi-Sugeno模糊模型描述的复杂非线性系统,同时考虑其存在参数不确定性以及时变时滞的情形,给出系统有限时间有界的充分条件.在一般传统H∞滤波器设计的基础上,结合有限时间有界的概念,导出保证系统在有限时间内,其滤波误差能量小于一个给定上界的H∞滤波器设计方...     

具有死区输入的分数阶混沌系统的有限时间同步

本文提出一种新型分数阶滑模控制方案来实现两个不同分数阶混沌系统的有限时间同步. 首先, 根据实际情况, 在研究系统同步过程中, 充分考虑死区非线性输入、参数不确定性、模型不确定性以及外界扰动对系统的影 响, 然后, 采用Lyapunov稳定理论证明滑模阶段和趋近阶段均是有限时间收敛的, 最后, 给出一个仿真实例充分验证本文所提出控制策略的有效性和可行性.     

一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

线性时变系统有限时间稳定性分析

针对一般非线性时变系统的有限时间稳定性分析问题,考虑到系统初始时刻在有限时间区间内的变化,本文分别提出了一般非线性时变系统的一致有限时间稳定性,一致收缩稳定性和固定调节时间一致收缩稳定性定义.针对一类线性时变系统,基于计算系统的所有轨线的包线的思想,本文分别给出了判定该类系统的收缩稳定性、固定调节时间收缩稳定性、一致有限时间稳定性、一致收缩稳定性、固定调节时间一致收缩稳定性的充分必要条件,同时给出了判定该类系统一致收缩稳定性及固定调节时间一致收缩稳定性的3个充分条件.进一步,本文将所得定理结果推广到了周期线性时变系统,所得结论为判定周期线性时变系统关于任意初始时刻的一致有限时间稳定性,一致收缩稳定性及固定调节时间一致收缩稳定性提供了理论依据.最后,以4个数值算例和两航天器相对运动过程为例验证了本文结果的正确性.     

分数阶Rucklidge系统复杂度分析及有限时间同步

Nonlinear system is a complex subject in the field of finance, and its complexity change and control methods have always been the key and difficult research points for experts and scholars. Earlier studies of nonlinear systems were based on integer-order nonlinear systems. With the deepening of the research onfractional-order systems, people have gradually realized that the complexity offractional-order systems is generally higher than that of integer-order systems. Analyzing and studying its complex characteristics is helpful to define system parameters and increase the complexity of the system. This paper takes a fractional Rucklidge system as an example to study its dynamic and complex characteristics. For the fractional-order nonlinear system, a synchronous controller is designed, which can be controlled and simulated synchronously. Simulation results show that the controller can achieve synchronization in a short time.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

Finite‐time stability of fractional order impulsive switched systems

This paper considers the finite‐time stability of fractional order impulsive switched systems. First, by using the fractional order Lyapunov function, Mittag–Leffler function, and Gronwall–Bellman lemma, two sufficient conditions are given to verify the finite‐time stability of fractional order nonlinear systems. Then, the concept of finite‐time stability is extended to fractional order impulsive switched systems. A sufficient condition is given to verify the finite‐time stability of fractional order impulsive switched systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Stabilization of uncertain fractional order system with time‐varying delay using BMI approach

This paper considers the systematic design of robust stabilizing state feedback controllers for fractional order nonlinear systems with time‐varying delay being possibly unbounded. By using the fractional Halanay inequality and the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of bilinear matrix inequalities are derived. The controllers can then be obtained by computing the gain matrices. In order to derive the gain matrices, two algorithms are proposed by using the existing computationally linear matrix inequality techniques. Two numerical examples with simulation results are provided to demonstrate the effectiveness of the obtained results.     

分数阶时滞非线性多智能体系统的自适应控制

针对分数阶多智能体系统中存在时滞和非线性特性, 时滞往往会引起控制系统的性能下降甚至出现系统 不稳定等问题, 提出了一种含时滞非线性的分数阶多智能体系统自适应控制方法. 对于多智能体系统的控制协议, 设计了基于领导者和相邻智能体状态信息的自适应控制协议, 减小了过大常数控制增益带来的能源浪费. 对于一 致性, 利用图论基础、分数阶Halanay不等式稳定性定理、Kronecker积和Schur补引理, 获得了分数阶时滞非线性多 智能体系统的LMI一致性条件. 仿真结果验证了本文算法的正确性和有效性. 由于整数阶系统是分数阶系统的特殊 形式, 本文结论可以直接推广到整数阶多智能体系统中.     

Caputo分数阶切换线性系统的指数稳定性

众所周知,与整数阶切换系统不同, Caputo分数阶切换系统的积分下界不能随子系统的切换而被更新,意味着在下界非一致的任意区间内不能直接取分数阶导数的分数阶积分.对此,本文给出了一个不等式(文中引理6)克服这一问题,并用1个数值例子进行了验证.通过这一不等式,然后分别利用多Lyapunov函数方法和模型依赖平均驻留时间(MDADT)方法,给出了Caputo分数阶切换线性系统指数稳定的条件,并利用2个数值例子进行验证.     

Adaptive tracking control for uncertain switched systems under asynchronous switching

This paper addresses the state‐tracking model reference adaptive control problem for a class of switched systems with parametric uncertainties, where switchings between subsystems and designed adaptive controller are asynchronous. First, we establish a stability criterion for a switched reference model and convert the state‐tracking problem into the stability problem of an error switched system. Then, an adaptive law is designed, and the global practical stability of the error switched system is guaranteed under a class of switching signals characterized by a dwell‐time condition. An electrohydraulic system is given as an example to demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite-time event-triggered control for a class of cascade switched affine nonlinear systems

This paper is concerned with the finite-time boundedness (FTB) problem of a class of cascade switched affine nonlinear systems. In order to avoid unnecessary waste of network communication and Zeno behavior, a dynamical event-triggered scheme is proposed, which is more general than some existing event-triggered schemes with a common parameter matrix. By using the average dwell time method and multiple Lyapunov function technologies, sufficient conditions for the existence of controller gains are first proposed such that the closed-loop system is finite-time bounded with a finite-time disturbance attenuation performance. It is also proved that the Zeno phenomenon is excluded. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

PDα‐type iterative learning control for fractional‐order linear continuous‐time switched systems

For a class of fractional‐order linear continuous‐time switched systems specified by an arbitrary switching rule, this paper proposes a PD^α‐type fractional‐order iterative learning control algorithm. For systems disturbed by bounded measurement noise, the robustness of PD^α‐type algorithm is first discussed in the iteration domain and the tracking performance is analyzed. Next, a sufficient condition for monotone convergence of the algorithm is studied when external noise is absent. The results of analysis and simulation illustrate the feasibility and effectiveness of the proposed control algorithm.     

二阶有向网络的鲁棒有限时间包容控制

在考虑非线性干扰和跟随者速度不可测的情况下,研究二阶有向网络的有限时间估计和鲁棒包容控制问题.提出含有估计层、控制层和跟随者层的新型分布式控制结构.应用有限时间稳定性理论和等效输出注入的思想,设计幂次估计器和滑模估计器,并给出网络误差的有限时间估计.进而采用齐次理论和滑模方法设计非光滑控制协议,驱使跟随者在有限时间内收敛并保持在领航者所构成的动态凸包中,且有效抑制干扰.仿真结果验证了理论分析的正确性.     

Input-to-state stability for discrete-time time-varying impulsive switched delayed systems with asynchronous phenomena

This paper studies the input-to-state stability (ISS) for a class of discrete-time time-varying impulsive switched delayed systems, in which the asynchronous phenomena are considered. Asynchronous phenomena here include two implications: asynchronous impulses and switches and asynchronous switching. The former means that the events, that is, impulses and switches, are not necessary to occur simultaneously, while the latter indicates that the actual switching modes and related controllers or specified modes do not coincide. Applying the mode-dependent concept to impulses and switches, both the improved Krasovskii-type and Razumikhin-type ISS criteria are provided. The time differences of Lyapunov functionals or functions here are sign-changing and time-varying, releasing from the traditional assumption that always requires negative definiteness. Meanwhile, in this paper, ISS or non-ISS subsystems and stabilizing or destabilizing impulses are taken into account. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.     

Finite-time quantised feedback asynchronously switched control of sampled-data switched linear systems

This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results.