正控制总量受限下离散线性系统的能控域

本文研究正控制总量受限下一类多输入离散线性系统的能控域问题.利用线性系统的分 解技巧、凸集的支撑超平面与阶的估计等方法,得到了能控域的结构性定理,还给出了状态属 于能控域的显式判别条件,这些结果在工程控制与社会经济系统中是有实用价值的.     

一般非线性系统的Kalman分解

本文讨论一般非线性系统的标准分解问题.线性系统的Kalman分解给出了系统的能控 状态、能观状态和系统的最小实现.本文首先给出非线性系统的局部第一类Kalman分解形 式,从而解决了系统的局部能控状态和局部能观状态的分解.然后,再给出第二类Kalmall分 解形式,它提供了非线性系统的局部最小实现.     

关于离散线性系统能决定性的判别

本文得到离散线性系统能决定性的一个判别定理,该定理解决了文献中尚未解决的相关问题。     

控制幅值受限下定常离散线性系统最小拍控制序列的一种综合方法

控制幅值受限下离散线性系统的最小拍控制问题与连续线性系统的快速控制问题是有很 大差别的,主要是它的非唯一性与非bang-bang性.文中用凸集的支撑超平面等方法研究了 能控域及其边界面的结构特性,给出了求解最小拍最小幅值控制序列综合解的一种计算方法, 该方法计算量较小,有实用价值.     

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。     

控制能量受限下离散线性系统能控域结构*

本文讨论控制器能量受限时,线性系统的能控域结构,并给出解析表达式。     

分数阶线性系统的稳定性证明

提出一种分数阶线性系统稳定性证明方法。首先分析了双参数Mittag-Leffler函数估值定理中的限制条件, 通过证明得出了该定理收敛域有误, 因此改进了双参数Mittag-Leffler函数估值定理, 并将它的参数由实数推广到矩阵。然后提出了可适用于分数阶线性系统的稳定性理论, 并利用改进的双参数Mittag-Leffler函数估值定理进行了证明。仿真结果验证了理论的正确性。     

能稳干扰解耦判据

本文提出用状态反馈实现线性定常系统能稳干扰解耦的一个判别准则.主要结果是定理 2,不仅给出了问题有解的充分必要条件,同时定理的证明过程也包含了判别的程序和状态反 馈矩阵K的求法.     

定常线性系统不同分解下状态变量之间的关系

本文以一般补空间的概念讨论定常线性系统的分解,指出取自然基作为补空间的基,可 以使系统分解的变换矩阵求逆最简单.鉴于在正交补空间定义下用交空间方法一般得不到 标准分解,本文给出了一种在一般补空间定义下利用交空间进行标准分解的方法,证明了基 本的不能控状态变量、基本的能观状态变量和基本的能观不能控状态变量的不变性.     

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。     

Controllability of linear time-invariant systems

In this paper it is shown that for any controllable linear time-invariant system, an arbitrary initial point can be driven to an arbitrary final point by means of an input, polynomial in t of degree 2k— I, with k the controllability index of the system. Also, the state trajectory is polynomial in time and of the same degree. The bound on the degree is an improvement with respect to similar results in the literature. The proof of this result is rather direct compared to the involved proof in the literature of a weaker theorem. An extension of this result considering sinusoidal inputs and state trajectories is provided.     

Controllable regions of linear systems with bounded inputs

It is known that the controllable region of a general unstable system with bounded control is the Cartesian product of the controllable region of its subsystem with antistable modes and that of its subsystem with stable and marginally stable modes. While the controllable region of a system with only stable and marginally stable modes is well known to be the whole state space, that of an antistable system is studied in this paper. A necessary and sufficient condition for a state of an antistable system to be controllable is given. The boundary of the controllable region is characterized.     

Impulsive semilinear heat equation with delay in control and in state

In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable. After that, we add impulses and a nonlinear perturbation with delay in state, and using Rothe's fixed point theorem, we prove that the interior approximate controllability of the impulsive semilinear system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear diffusion process in Hilbert spaces with delay in control and in state.     

Comments "On pole assignment in multi-input controllable linear systems"

A short and direct new proof is given to Wonham's theorem that a time invariant multi-input linear dynamical system is controllable only if its poles can arbitrarily be reassigned in a closed-loop system by means of a constant (state variable) feedback law. The construction provided in the proof is directly applicable as an effective algorithm for this pole assignment.     

Controllability and stabilizability of switched linear-systems

In this paper, we study the conjecture made in (IEEE Trans. Automat. Control 47 (8) (2002) 1401) concerning the existence of basic switching sequence for switched systems, and give it an affirmative answer and a construction method. This paper proves that for switched linear system, there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system. Hence, the controllability can be realized by using only one switching sequence. Then, the result is extended to the systems with time-delay in controls. Furthermore, we define the stabilizability of switched linear systems, and based on certain transformation of state coordinate, we give a necessary and sufficient condition for the stabilizability. Two examples are presented to illustrate the obtained results.     

Control and state observation of periodic linear multimodal systems

This paper investigates the control and state observation problem for periodic linear controllable and observable multimodal systems. For a controllable periodic linear multimodal system, this paper proposes an alternative minimum-norm dynamic state feedback control scheme for state transition matrix assignment. Also presented is a new design of state observers for an observable periodic linear multimodal system. Finally, an analysis of closed-loop behaviour of controlled periodic linear multimodal systems using a state-estimate is given     

Kalman controllability decompositions for differential-algebraic systems

We study linear differential-algebraic control systems and investigate decompositions with respect to controllability properties. We show that the augmented Wong sequences can be exploited for a transformation of the system into a Kalman controllability decomposition (KCD). The KCD decouples the system into a completely controllable part, an uncontrollable part given by an ordinary differential equation and an inconsistent part, which is behaviorally controllable but contains no completely controllable part. This decomposition improves a known KCD from a behavioral point of view. We conclude the paper with some features of the KCD in the case of regular systems.     

Parallel concatenated convolutional codes from linear systems theory viewpoint

The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input–state–output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.     

On partitioned controllability of switched linear systems

When a switched linear system is not completely controllable, the controllability subspace is not enough to describe the controllability of the system over whole state space. In this case the state space can be divided into two or three control-invariant sub-manifolds, which form a control-related partition of the state space. This paper investigates when each component is a controllable sub-manifold. First, we consider when a sub-manifold is controllable for no control input case. Then the results are used to produce a necessary and sufficient condition assuring the controllability of the partitioned control-invariant sub-manifolds of a class of switched linear systems. An example is given to demonstrate the effectiveness of the results.