带有非线性扰动的不确定切换系统鲁棒控制

针对一类非线性扰动项不满足匹配条件的不确定切换系统鲁棒状态反馈镇定问题,采用单李雅普诺夫函数和多李雅普诺夫函数方法,研究了状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性,而且有外界干扰的切换系统,分别给出了不确定切换系统鲁棒可稳的充分条件。仿真结果表明,所设计的两类控制器及相应的切换策略均能保证闭环系统渐近稳定。     

线性周期性切换系统的镇定及鲁棒镇定研究

针对线性周期性切换系统的镇定及鲁棒镇定问题,分别研究了确定的和结构不确定的线性周期性切换系统,利用状态反馈镇定或鲁棒镇定了该类系统。在镇定控制器的设计中使用了LMI方法,仿真实验验证了控制器的设计方法有效。     

一类不确定线性切换系统的二次鲁棒稳定性

为了研究一类线性切换系统及其带有非线性扰动系统在任意切换律下的二次鲁棒稳定性问题,采用Riccati不等式导出了带有时变扰动的在任意切换律下二次鲁棒稳定的充分条件,利用线性矩阵不等式研究了其带非线性扰动项的系统在任意切换律下的二次鲁棒稳定的充分条件,并用数值例子对所得结果加以仿真。结果表明,所得的结果是正确的。     

参数不确定广义系统鲁棒H∞容错控制器的设计

研究了一类不确定广义系统基于状态反馈针对执行器发生故障的鲁棒H∞容错控制问题；运用线性矩阵不等式(LMI)给出了鲁棒H∞容错控制器存在的充分条件；通过假设失效的执行器的输出信号是任意的能量有界干扰信号，将不确定广义系统的鲁棒H∞容错控制问题化为H。控制问题，给出了该问题可解性的充分奈件。鲁棒H∞容错控制器可以通过解相应的线性矩阵不等式(LMI)给出，因而具有数值易解性。最后，所给的设计例子说明了方法的有效性。     

传感器增益故障下鲁棒可靠控制

针对电力系统中传感器发生增益故障情况下,一类参数不确定离散时滞系统的静态输出反馈保成本可靠控制器设计问题。系统中的参数不确定性满足广义匹配条件。根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了含有时滞记忆和无时滞静态输出反馈保成本鲁棒可靠控制律的存在条件。通过求解一组线性矩阵不等式,可以得到使得闭环保成本上界最小的鲁棒可靠控制器。最后通过电力系统仿真示例说明所提出方法的正确性。     

带非线性参数摄动不确定系统的鲁棒(D)稳定和鲁棒镇定

为了研究带二次不确定参数线性系统的鲁棒够稳定和鲁棒镇定问题,考虑了D域为复平面左半平面的圆盘域,并采用线性矩阵不等式（LMI）方法,证明该系统鲁棒D稳定的充分条件等价于一个线性矩阵不等式的可解性问题,利用该LMI的可行解可求得了系统鲁棒镇定状态反馈控制器。通过实例说明了该方法的有效性。     

中立型时滞系统基于观测器的控制器设计

针对一类线性不确定中立型时滞系统的状态观测器和基于观测器的鲁棒控制器设计问题,通过构造增广系统,基于线性矩阵不等式的方法,椎导了此类不确定系统状态观测器和基于观测器的鲁棒控制器存在的时滞相关充分条件,同时给出了相应的状态观测器和基于观测器的鲁棒控制器的求解。数值实例证明了该设计方案的可行性。     

一类不确定时滞系统的输出反馈镇定

对于控制通道中存在时滞的不确定时滞系统，讨论了时滞独立的输出反馈镇定律的设计问题，利用线性矩阵不等式方法给出了鲁棒镇定律的存在条件及镇定律存在时相应的镇定律设计方法，研究结果表明，针对控制通道中存在时滞的一类不确定系统，在一定条件下可以利用线性矩阵不等式方法设计输出反馈镇定律。文中给出了算例以说明方法的应用。     

不确定滞后系统的鲁棒模型预测控制

对于输入受约束的离散不确定滞后系统，提出鲁棒模型预测控制方法，其中不确定性存在于系统的状态矩阵和输入矩阵当中，且满足范数有界条件。用LMI解决滞后系统的不确定性和约束，针对滞后系统给出了新的鲁棒性能指标上界和系统稳定的充分条件，通过求解LMI凸优化得到状态反馈控制律，对提出的方法进行了数字仿真研究，结果表明，基于LMI约束不确定滞后系统的鲁棒模型预测控制易于求解。适于实际应用。     

Lurie型不确定多时滞系统的时滞相关鲁棒绝对稳定性

研究了一类状态和控制具有不确定多时滞的、更加一般的Lurie型系统的鲁棒绝对稳定性,其中时滞是未知定常,不确定是范数有界的。通过Lyapunov泛函和线性矩阵不等式方法,得到了以线性矩阵不等式方式给出的时滞相关鲁棒稳定性充分条件。示例表明了本文结果的有效性。     

离散时延切换系统的鲁棒控制

针对一类子系统为离散时延系统并且参数具有不确定性的切换系统,研究了鲁棒控制以及H∞扰动抑制问题。通过为每个子系统施加状态反馈并基于多李雅普诺夫函数法,分别给出了保证闭环系统渐近稳定的鲁棒控制器以及具有H∞扰动抑制性能控制器的设计方法。控制器参数可通过一组矩阵不等式获得,使用将待解不等式转化为双线性矩阵不等式并采用巡回迭代算法对其求解。通过仿真例子说明了设计方法的有效性。     

Finite-time asynchronous control of linear time-varying switched systems

In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.     

不确定关联时滞广义大系统的分散鲁棒镇定

为了研究一类不确定性关联时滞广义大系统的分散鲁棒镇定问题,根据广义系统理论,采用线性矩阵不等式方法,研究了不确定性关联时滞广义大系统的鲁棒稳定性和分散鲁棒镇定控制器设计,分别导出了不确定性关联时滞广义大系统的鲁棒稳定和分散鲁棒镇定的充分条件,且都是一组严格的线性矩阵不等式。当条件成立时给出了分散鲁棒反馈控制律的表示式,并用数值实例对所得结果加以仿真,结果表明所得方法是有效的。     

Energy efficient nonfragile control protocol for nonlinear large-scale systems with input quantization

The problem of robust stabilization for a class of nonlinear large-scale systems with the energy constraints and time-varying actuator faults is addressed in this article. In the considered system, the stabilization criteria is achieved via a sensor-network-based distributed fault-tolerant controller. Moreover to limit the consumption of energy by the sensors, the measurement size reduction technique and communication rate reduction approach are implemented such that the resulting closed-loop system is stable within a predefined extended passive performance index level. In particular, the sensor signal quantization technique is used to reduce the frequency and size of the transmitted data packet in the communication sequence. Based on the switched system theory and Lyapunov approach, a new set of sufficient conditions is obtained in the form of linear matrix inequality constraints to ensure the exponential stabilization of the considered system. The developed fault-tolerant resilient control gains are designed by resorting to the cone complementarity linearization algorithm. Moreover, a nonisothermal continuous stirred-tank reactor with interconnection is considered as an example to demonstrate the effectiveness of the proposed design technique.     

Stability and stabilization in switched discrete‐time systems

In this paper, we investigate the stability and stabilization problem for discrete‐time switched systems. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. The relationship between the developed model of the switched system and the Markovian jump system is analyzed. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of a linear matrix inequality. Then, we extend the results to a more practical case where the subsystem occurrence probabilities of switching are known to be constant, but their specific values are only known with some uncertainty. A new iterative approach is employed to choose the switching law between the subsystems. For unstable switched systems, mode‐dependent state feedback and static output feedback controllers are developed to achieve the stabilization objective. Finally, several simulation examples are presented to show the efficacy of the proposed criteria and methods. Copyright © 2012 John Wiley & Sons, Ltd.     

离散时间状态反馈切换系统的稳定性分析

针对线性离散时间切换系统,提出了基于切换观测器的状态反馈系统的稳定化方法;分析了含有观测器的状态反馈闭环系统的稳定性,得出了线性离散时间切换系统利用状态反馈稳定化一个充分条件,并用线性矩阵不等式理论给出了观测器增益矩阵和状态反馈增益矩阵的算法,最后给出了一个仿真例子,以说明结论的正确性.