随机跳变摄动系统的鲁棒H∞ 控制

针对具有独立马尔科夫结构的线性随机跳变摄动系统,在小时间参数不为零的基础上研究了系统的鲁棒 ∞控制问题.首先提出具有线性矩阵不等式形式的鲁棒 ∞稳定判据;进而,在计算相应小时间参数上界的基础上给出线性随机跳变摄动系统的状态反馈鲁棒 ∞控制方法.对于任意处于小时间参数上界范围内的数值,所提出的方法均可确保相应的闭环系统具有鲁棒 ∞性能.     

一类不确定离散系统的严格正实分析和设计

考虑了一类不确定离散多变量系统严格正实分析和控制问题,其中不确定参数具有非负性.分析了系统鲁棒稳定且严格正实的条件,讨论了状态反馈、输出反馈使闭环系统鲁棒稳定且严格正实的问题.将不确定系统的鲁棒严格正实分析和设计转化为确定系统的严格正实分析和控制,得到了系统鲁棒稳定且严格正实的充分必要条件.最后给出了鲁棒严格正实控制问题的可解条件及控制器的综合方法.     

不确定时变采样数据系统的鲁棒H∞滤波

研究了一类时变采样不确定系统的鲁棒H∞滤波问题。视参数不确定性为外部扰动，通过构造辅助信号，将不确定时变采样数据系统的鲁棒H∞滤波转化为确定性时变采样数据系统的H∞滤波问题，然后利用离散跳变系统的有界实引理，提出了不确定时变采样数据系统的鲁棒H∞滤波的新定理。滤波器的存在性等价于一组带有限离散跳变的Riccat方程有解性，同时给出了滤波器的参数化设计方法。方法的主要优点是：在鲁棒H∞滤波器存在性定理的证明过程中。通过寻找适当的尺度因子将鲁棒滤波问题转化为等价的确定性滤波问题，没有采用不等式关系。从而避免了同类研究中复杂的证明过程。     

独立摄动参数不确定线性系统的正实控制

考虑了一类范数有界参数不确定线性系统的鲁棒正实性分析和设计问题，其中参数不确定性是独立摄动的．通过构造增广系统将不确定系统的鲁棒正实分析和控制问题转化为确定系统的情形，给出了鲁棒正实分析问题的线性矩阵不等式解法，导出了输出反馈控制器的存在条件．所得结论将范数有界参数不确定系统的鲁棒正实分析和控制的现有结果推进了一步．     

一类参数不确定系统的鲁棒正实性

本文考虑了一类参数不确定系统的鲁棒正实性,给出了一个输出反馈系统具有鲁棒严格扩展正实性（ESPR）的充分条件以及求反馈控制器的方法。并利用该条件可估计出系统保持ESPR的最大参数撮动范围。在此基础上,对某不确定控制系统进行了鲁棒正实控制设计。并采用两种方法对结果进行验证,仿真的结果证明了该设计的有效性与可行性。     

二次型耗散线性离散系统的鲁棒性分析与控制

考虑一类不确定离散多变量系统的鲁棒二次型耗散性分析和控制,其中各不确定参数矩阵具有线性分式形式.首先对确定系统建立二次型耗散性与正实性之间的等价关系,由此导出线性系统二次型耗散的充分必要条件;然后证明不确定系统的鲁棒耗散性分析和控制可转化为确定系统的耗散性分析和设计,给出了这类不确定系统鲁棒耗散的充分必要条件以及鲁棒耗散控制问题的线性矩阵不等式解法.所得结果可将H∞控制与正实控制统一起来,提供一种较为灵活、保守性较小的系统设计方法.仿真例子说明了所提方法的有效性.     

不确定跳变系统鲁棒L 2-L ∞滤波

针对既有连续时间演化,又含Markov事件驱动的一类混杂动态跳变系统,研究L2-L∞性能指标下的鲁棒滤波问题,只要系统遭受的外部干扰是能量有界的,便可保证一定的预设滤波误差峰值水平.在有限时间域内定义L2-L∞增益,利用随机稳定性分析获得了若干主要结果.鲁棒滤波器的分析和设计,不仅考虑了各模态下凸多面体形式描述的动态系统参数不确定性,更考虑了各模态间跳变转移概率的不确定性,使得滤波器对模态跳变机理具备了一定的鲁棒性.鲁棒滤波器的存在条件及设计方法可直接利用耦合线性矩阵不等式.最后用数值示例对结果进行了验证.     

奇异线性随机跳变系统有界误差估计器设计

从随机稳定的基本定义开始,对奇异线性随机跳变系统的随机稳定问题进行分析,推导出满足鲁棒∞性能的随机稳定条件,并在此基础上进行推广.首先针对估计误差满足鲁棒∞性能约束的条件,给出带Kalman滤波器形式的滤波器设计方法;然后重点研究了系统中各模态参数矩阵带有不确定性的情况;最后给出相应的数值算例并计算滤波器系数,验证了该方法的有效性和正确性.     

参数不确定马尔可夫跳变系统的鲁棒适应控制

针对具有参数不确定的线性马尔可夫跳变系统的鲁棒适应控制问题进行了研究.分析了切换系统切换律的可观测和不可观测情形.对于可观测的切换律,利用线性矩阵不等式和共同二次Lyapunov函数方法,得出的具有参数不确定的切换系统是鲁棒可镇定的;对于切换律符合不可观测的马尔可夫随机过程的情况,通过设计恰当的采样适应控制器得到系统随机可镇定的充分条件.并通过例子给出适应镇定控制器的算法.     

具有随机丢包的关联系统的分散控制

研究了在子系统之间信息传输存在随机丢包现象时关联大系统的性能分析及控制器设计问题. 通过引入空间变量及空间移动算子, 将关联系统建模成具有Markovian跳变参数的关于离散时间变量和空间变量的多维系统, 结合跳变系统有界实引理, 得到使整个关联系统均方稳定并满足一定性能指标的解析条件. 然后基于线性矩阵不等式变换给出确保关联大系统鲁棒均方稳定性的一种分散输出反馈控制器的设计方法. 最后通过一组多机器人直线编队的例子说明本文算法的正确性和有效性.     

On stabilization of bilinear uncertain time-delay stochasticsystems with Markovian jumping parameters

In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulation     

Security control of positive semi‑Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourntime distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.     

鲁棒严格正实控制器设计

基于强严格正实引理使用线性矩阵不等式方法讨论了参数不确定线性系统鲁棒严格正实控制器的综合问题,提出了二次严格正实的新概念,证明了静态状态反馈解的存在性,并给出了状态反馈壮次严格正实控制器的存在条件和综合方法。     

Stability analysis and stabilization of networked linear systems with random packet losses

This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.     

Guaranteed cost control of uncertain discrete‐time singular Markov jump systems with indefinite quadratic cost

The guaranteed cost control problem for discrete‐time singular Markov jump systems with parameter uncertainties is discussed. The weighting matrix in quadratic cost function is indefinite. For full and partial knowledge of transition probabilities cases, state feedback controllers are designed based on linear matrix inequalities method which guarantee that the closed‐loop discrete‐time singular Markov jump systems are regular, causal and robust stochastically stable, and the cost value has a zero lower bound and a finite upper bound. A numerical example to illustrate the effectiveness of the method is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. 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. Simulation results illustrate the effectiveness of the developed approaches.     

一类具有Markov跳跃参数的不确定线性跳跃系统鲁棒非脆弱H∞控制问题研究

This paper describes the synthesis of robust and non-fragile H∞ state feedback controllers for a class of uncertain jump linear systems with Markovian jumping parameters and state multiplicative noises. Under the assumption of a complete access to the norm-bounds of the system uncertainties and controller gain variations, sufficient conditions on the existence of robust stochastic stability and γ-disturbanee attenuation H∞ property are presented. A key feature of this scheme is that the gain matrices of controller are only based on lt, the observed projection of the current regime rt.     

Reliable dissipative control for stochastic impulsive systems

This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly (Q,S,R)-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on H^∞ control.     

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.