非线性控制系统的特性（I）

本文采用与线性系统理论相比较的方法，阐述非线性控制系统理论。文中通过一些例子来分析非线性控制系统在能控性，能观性，抗干扰性，解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法，论述和结论上的特点。第一部分介绍非线性系统的能控性和能观性。     

非线性控制系统的特性（Ⅰ）

本文采用与线性系统理论相比较的方法，阐述非线性控制系统理论。文中通过一些例子来分析非线性控制系统在能控性、能观性、抗干扰性、解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法、论述和结论上的特点。第一部分介绍非线性系统的能控性和能观性。     

感应电动机系统的能控性与能观测性分析

分析了感应电动机系统的能控性与能观测性。结果表明系统是弱能控与弱能观的。而且,采用非线性状态反馈解耦控制和非线性坐标变换后的局部闭环解耦线性系统是能控与能观的。     

线性连续定常系统状态比例积分反馈控制

在状态反馈控制的基础上 ,提出了状态比例积分反馈控制的概念 ,并证明了线性定常系统状态比例积分反馈控制系统的能控性、能观性和稳定性的充要条件     

一般模型2-D系统的观测器设计理论

该文讨论了2-D一般模型(2DGM)在标准边界条件下的渐近观测器的存在性条件及其 设计问题.为此,首先将由Bisiacco等人在1985年发展起来的相应于对角边界条件的2-D、 渐近稳定性理论推广到了具有标准边界条件的2-D一般模型.在此基础上,借助于局部能控 性概念,建立了一系列十分类似于1-D情形的观测器的存在条件,从这些存在条件出发也可 以得到相应的观测器设计算法,最后还得出了2DGM的分离性定理.     

有界区域上Petrowsky系统的能控性和能稳性

利用D.L.Russel关于“能稳性导致能控性”的论断,研究Petrow sky系统的能控性,首先取线性反馈控制,得到线性反馈Petrow sky系统的能量的指数衰减,从而由D.L.Russel的“能稳性导致能控性”的论断得到能控性.其次取非线性反馈控制,得到Petrow sky系统的一些能量估计,但是不能得到指数能稳.     

周期性系统的能控性理论

主要探讨周期性系统(包括连续和离散两种情形)的能控性问题，对文献中有关周期为To的连续周期性系统的能控性结论进行了完善，推导出系统能控等价于单周期(0，To)内能控的结论，并将这些结论直接推广到离散周期性系统；然后讨论了离散前后周期性系统能控性保持不变的可能性，证明在采用不等间距采样方式时，离散前后周期性系统的能控性保持不变。     

广义对称组合系统的结构分析

研究了由若干个相同的广义线性子系统以对称的内联方式构成的广义对称组合大系统的性质.首先,通过系统变换,将原广义对称组合大系统转换为两个低阶的修正子系统,然后通过分析得到广义对称组合大系统的稳定性、能控性、能观性、固定模的存在性、分散正常化、Lyapunov方程和Riccati方程的解等性质,均可由这两个低阶的修正子系统的相应性质来描述.     

一类无穷维半线性系统能控的充分必要条件

本文给出无穷维半线性系统能控的充分必要条件及其应用。     

线性连续定常系统状态比例积分反馈控制

在状态反馈控制的基础上,提出了状态比例积分反馈控制的理论,并证明了线性定常系统状态比例积分反馈控制系统的能控性、能观性和稳定性的充分条件。     

Structural controllability of switched linear systems

This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems’ state matrices are either unknown or zero. The structural controllability is a generalization of the traditional controllability concept for dynamical systems and purely based on the interconnection relation between the state variables and inputs through non-zero elements in the state matrices. In order to illustrate such a relationship, two kinds of graphic representations of switched linear systems are proposed, based on which graph theory-based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented. Finally, the paper concludes with discussions on the results and future work.     

一类离散双线性系统可控性研究

在工程中, 系统离散化前后可控性是否一致是一个重要问题. 近来, Elliott就一类双线性系统, 首次构造出了一个连续时不可控、但经离散化后可控的二阶反例. 鉴于离散化后的系统可控性无法利用已有方法进行判断, 本文给出了一个二阶离散双线性系统可控性的充分条件, 从而在更一般情形下得到了一类连续时系统不可控, 离散化后可控的反例, 深化了对双线性系统可控性的认识. 进而, 本文证明了对于该类系统, 当其阶数大于2时, 可控性反例不再存在.     

随机系统的能稳性和精确能控性的关系

研究了随机系统的能稳性和精确能控性的关系,象确定性情形一样,我们证明了在随机情形下,精确能控性蕴涵着的能稳性。     

The Controllability,Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.      

Controllability of heterogeneous multiagent systems

The existing results on controllability of multiagent systems (MASs) are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous MASs, where the agents are modeled as two types. One type is that the agents have the same high‐order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different; the other type is that the agents have generic linear dynamics, and the dynamics are supposed to be heterogeneous. For the first type, the necessary and sufficient condition for controllability of heterogeneous‐topology system is derived via combination of Laplacian matrices. For the second type, the contribution also has two parts. The first part supposes that the agents have the same dimensional states and proves that controllability of this kind of MASs is equivalent to the controllability of each node and the whole interconnection topology, while the last parameter of the state feedback vector must not be 0. The second part supposes that the agents may have different dimensional states. For this kind of systems, the concept of β‐controllability is proposed. The necessary and sufficient condition for β‐controllability of heterogeneous‐dynamic systems is also derived and it is also proved that the feedback gain vectors have the effect to improve controllability. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper.     

On controllability and stabilizability of probabilistic Boolean control networks

The controllability of probabilistic Boolean control networks(PBCNs)is first considered.Using the input-state incidence matrices of all models,we propose a reachability matrix to characterize the joint reachability.Then we prove that the joint reachability and the controllability of PBCNs are equivalent,which leads to a necessary and sufcient condition of the controllability.Then,the result of controllability is used to investigate the stability of probabilistic Boolean networks(PBNs)and the stabilization of PBCNs.A necessary and sufcient condition for the stability of PBNs is obtained first.By introducing the control-fixed point of Boolean control networks(BCNs),the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of PBCNs.Both necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix,which are easily computable.Hence the two necessary and sufcient conditions are straightforward verifiable.Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.     

广义系统能控性的几个注记

本文首先给出了广义系统能控性与正常系统能控性的关系,并由此讨论了广义系统最优 经济结构综合问题及能控性程度的度量形式.最后给出了工程算例.     

Controllability of piecewise linear systems

The paper deals with a discontinuous control system that consists of two finite-dimensional linear systems; the first describes the motion in a given half-space, the second in the complementary half-space. Necessary and sufficient conditions for local controllability are obtained.     

On Near‐controllability of Discrete‐time Upper‐triangular Bilinear Systems with Applications to Controllability

Near‐controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been demonstrated on two classes of discrete‐time bilinear systems. This paper studies near‐controllability of discrete‐time upper‐triangular bilinear systems, which are uncontrollable and are more general than the two classes mentioned. A necessary and sufficient condition for the systems in dimension two to be nearly controllable is presented, which covers the existing results. For the systems with high dimensions, necessary conditions and sufficient conditions of near‐controllability are provided, which generalize the existing results. In particular, the obtained near‐controllability results are applied to controllability of discrete‐time bilinear systems. An example also is given to demonstrate the effectiveness, which shows that the controllability problems of discrete‐time bilinear systems can be solved by near‐controllability.     

Controllability for a Class of Parallelly Connected Polynomial Systems

Null controllability for a class of parallelly connected discrete-time polynomial systems is considered. We prove for this class of systems that a necessary and sufficient condition for null controllability of the parallel connection is that all its subsystems are null controllable. Consequently, the controllability test splits into a number of easy-to-check tests for the subsystems. The test for complete controllability is also presented and it is subtly different from the null controllability test. A similar statement is then given for complete controllability of a class of parallelly connected continuous-time polynomial systems. The result is somewhat unexpected when compared with the classical linear systems result. We identify the phenomenon which shows the difference between the linear and nonlinear cases. Date received: January 22, 1997. Date revised: January 14, 1998.