伺服问题的二自由度镇定控制器参数化

对于多输入多输出四块线性系统,本文研究了存在跟踪和干扰抑制约束的二自由度镇定控制器参数化问题,给出了一般条件下的伺服问题二自由度镇定控制器参数化表示。     

基于信噪比受限通道的网络控制系统镇定

研究了同时考虑通信和网络特性的线性系统镇定问题.首先针对连续时间网络控制系统,使用线性矩阵不等式方法得到了系统镇定所需要的最小信噪比;然后将问题推广到一类更为复杂的离散时间异构网络控制系统并得到了相似的结论.其中建立的多传感器随机时滞模型很好地刻画了token-passing总线控制网络,它更具有实际意义;最后通过数值例子对以上理论进行了仿真验证,有效表明了系统镇定时被控对象不稳定极点、网络时滞和信噪比之间的关系.     

同时镇定问题的一个数值解法*

本文运用多项式稳定性充分判据，将不同阶次线性系统的同时镇定问题化成非线性不等式组的求解，然后提出求解不等式组的拟牛顿下山数值法，并应用于同时镇定问题中，算例表明该方法的有效性。     

镇定网络化线性系统的数据率定理

传统控制理论研究如何利用反馈信息实现控制目标,且通常假定通信链路的物理局限性对控制系统没有显著影响.通信理论研究如何将信息从信道的一端可靠地传输到另一端,但忽略传输信息的具体用途.因此,控制和通信在过去是两门相对独立发展的学科.网络化控制系统的涌现促使研究者综合利用控制和通信理论来刻画反馈通信网络对控制系统的影响.本文回顾了基于数字通信网络的离散线性系统的可镇定性问题.特别地,基于信息理论的控制方法,讨论了镇定网络化线性系统所需的最低通信数据率问题.结果表明,最低数据率本质上取决于开环系统的拓扑熵率.     

线性系统时滞反馈镇定研究

本文研究线性系统状态反馈控制存在延迟时的镇定问题.对于一般情形下的时滞镇定问 题的判定,提出了一个充分条件;对于具有不稳定单根的单输入控制系统,提出了时滞镇定一 个构造性的充分条件;并讨论了时滞反馈镇定控制器的实现问题.     

执行器失效不确定时滞系统的指定衰减度鲁棒可靠控制

针对一类含有时变时滞的不确定参数线性系统,研究了在执行器发生故障情况下的鲁棒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,时变时滞的大小及其变化率有界,并假设故障执行器元件的输出为零.经过适当的模型变换,将原系统的鲁棒指数镇定问题转化为另一个等价系统的鲁棒镇定问题.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了鲁棒可靠控制器存在的时滞无关和时滞相关充分条件.仿真结果表明了该控制器设计方法的有效性.     

一类非线性系统的量化控制器的设计

研究了一类非线性离散系统的量化反馈控制.对于一类满足齐次性质的非线性系统,针对有界的初始状态,我们设计了具有可数个固定控制输入的控制方式,实现了用"可数"去镇定"不可数"这一控制问题.值得指出的是,我们的结论可以直接应用到线性的情形,并与已有的关于线性系统的结论保持一致.同时,给出了例子验证了结论的有效性.     

一类不确定时滞系统的时滞依赖型鲁棒控制器设计

本文研究了一类状态和控制同时存在滞后的不确定线性系统时滞依赖型鲁棒镇定２，针对所有容许的时变未知但有界的不确定性，得到了一种新的确保系统可鲁棒镇定的充分条件和相应的鲁棒镇定控制器设计方法，所得到的结果与时滞相关的，并且以线性矩阵不等式（ＬＭＩ）形式给出。     

带有常数干扰的正则线性系统的镇定

本文考虑带有常数干扰的抽象正则线性系统的状态反馈镇定问题.本文控制设计采用线性系统的动态补偿方法,将传统的PID控制推广到无穷维正则线性系统.通过引入积分作用,控制器可以有效地补偿常数干扰.论文给出了具体的状态反馈法则,并证明了对应闭环系统的指数稳定性.理论结果被应用于带有常数干扰的不稳定热方程,给出了控制器及其闭环系统的指数稳定性,数值仿真验证了本文理论结果的有效性.     

线性时滞系统的时滞相关鲁棒控制

讨论了同时具有输入时滞与状态时滞的线性系统的时滞相关鲁棒控制问题.将矩阵分解思想应用于线性时滞系统的控制综合,借助于积分不等式,利用Lyapunov_Krasovskii泛函方法,得到了系统经无记忆状态反馈后可镇定的、基于LMI的时滞相关条件.既不要对原系统进行模型变换,也不要对交叉项进行界定.最后的实例说明了本文方法的有效性.     

Rank-one LMI approach to simultaneous stabilization of linear systems

Following a polynomial approach to control design, the simultaneous stabilization by a controller of given fixed order of a family of SISO linear systems is interpreted as an NP-hard BMI feasibility problem. Upon formulating this BMI problem as an LMI problem with an additional non-convex rank constraint, two simultaneous stabilization methods are then proposed. The first method is a heuristic algorithm performing rank minimization by potential reduction. The second method hinges upon necessary conditions and sufficient conditions for simultaneous stabilization derived from geometric properties of the intersection of a set of ellipsoids. Both methods are then illustrated by numerical examples.     

The transitivity in simultaneous stabilization

This paper deals with the transmission problem in simultaneous stabilization of time-varying linear systems. We establish two criteria for the transitivity in simultaneous stabilization. In particular, we give a necessary and sufficient condition for certain linear systems to satisfy a strengthened version of transitivity.     

Stabilization of linear strict-feedback systems with delayed integrators

The problem of compensation of input delays for unstable linear systems was solved in the late 1970s. Systems with simultaneous input and state delay have remained a challenge, although exponential stabilization has been solved for systems that are not exponentially unstable, such as chains of delayed integrators and systems in the ‘feedforward’ form. We consider a general system in strict-feedback form with delayed integrators, which is an example of a particularly challenging class of exponentially unstable systems with simultaneous input and state delays, and design a predictor feedback controller for this class of systems. Exponential stability is proven with the aid of a Lyapunov-Krasovskii functional that we construct using the PDE backstepping approach.     

Simultaneous controller design for time-varying linear systems

In this paper, we establish the parametrization of all simultaneously stabilizing controllers for two time-varying linear systems. A new approach to the simultaneous stabilization of three time-varying linear systems is also provided.     

Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.     

Computation of stabilizing Lag/Lead controller parameters

One of the central problems in control theory relates to the design of controllers for stabilization of systems. The paper deals with the problem of computing all stabilizing values of the parameters of Lag/Lead controllers for linear time-invariant plant stabilization. It is well known that linear controllers of Lag/Lead type are still widely used in many industrial applications. In this paper, an extension of a new approach to feedback stabilization based on the Hermite–Biehler theorem to the Lag/Lead controller structure is given. In addition, the problem of stabilization of uncertain systems defined by an interval plant is studied using the Kharitonov and the Hermite–Biehler theorems. The proposed method is analytical and it can be applied successfully using today’s advanced computer technology. Examples are included to illustrate the method presented.     

带有时变不确定性的线性系统族的同时镇定

本文考虑了具有时变不确定性的线性系统族的状态反馈同时二次镇定问题，这个问题能更全面地刻划考虑系统的不确定性，并将其转注多个ｙａｐｕｎｏｖ方程的同一解的问题，最后给出一个数值算例。     

Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel’s technique. We give a complete answer to the open problem proposed by Patel et al., which auto-matically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabiliz-ing controller design method is established. Our numerical examples significantly improve the relevant results in the literature.