Linear systems theory revisited

This paper investigates and clarifies how different definitions of reachability, observability, controllability, reconstructability and minimality that appear in the control literature, may be equivalent or different, depending on the type of linear system. The differences are caused by (1) whether or not the linear system has state dimensions that vary with time (2) bounds on the time axis of the linear system (3) whether or not the initial state is non-zero and (4) whether or not the system is time invariant. Also (5) time-reversibility of systems plays a role. Discrete-time linear strictly proper systems are considered. A recently published result is used to argue that all the results carry over to continuous time. Out of the investigation two types of definitions emerge. One type applies naturally to systems with constant dimensions while the other applies naturally to systems with variable dimensions. This paper reveals that time-varying (state) dimensions that are allowed to be zero are necessary to obtain equivalence between minimality and (weak) reachability together with observability at the systems level. Besides their theoretical significance the results of this paper are of practical importance for model reduction and control of time-varying discrete-time linear systems because they result in minimal realizations with smaller dimensions that are also computed more easily.     

仿射非线性系统的能控性

研究仿射非线性系统的能控性问题.利用向量场族对应的积分曲线定义系统的能控性,建立一个新的基于漂移向量场弱泊松稳定的能控性判据,并给出了完整的证明.利用该结论对定义在紧致黎曼流形上的解析系统,给出了漂移向量场为保守场条件下的能控性的充要条件,并用状态流形的紧致性证明了弱泊松稳定性的几个等价条件.进一步利用保守系统的判据给出了一般仿射非线性系统能控的充分条件,井应用所得结论分析了欠驱动航天器姿态系统的能控性.     

Robust controllability of linear stochastic uncertain systems

The paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems. We show that the controllability of a stochastic uncertain system can be characterized using solutions to a game-type differential Riccati equation.     

Multirate sampled-data systems: computing fast-rate models

This paper studies identification of a general multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and real-time implementation.     

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.     

一种功能级的可测试性测度

本文提出了一种功能级的可测试性测度FLTM(Functional Level Te-stability Measure).针对功能级的故障模型,FLTM引入了数据位可控性与数据通路状态可控性的概念.由于不同的故障效应可观度不一样,文中引入了故障效应可观度的概念.FLTM着重考虑了重汇聚扇出对电路可测性的影响,提出了一种加权的可测度计算方法.     

Controllability and Extendibility of Continuous Multi-dimensional Behaviors

A continuous multi-dimensional behavior is defined to be the solution space of a linear system of constant-coefficient partial differential equations. After revisiting the concepts of controllability and extendibility for systems of this type, the following main result is obtained: behaviors that are both controllable and extendable are characterized by a concatenation property that naturally generalizes the notion of strong controllability, originally introduced for two-dimensional discrete behaviors by Willems and the second author. Published online: April 2006     

On computation of supremal controllable, normal sublanguages

In this paper, we present an algorithm for the computation of the controllable, normal sublanguage of a given language, encountered in the solution of the supervisory control of discrete-event systems under partial observation. The algorithm produces the desired result under certain assumptions on the plant and the event projection map. In particular, the plant has to be nonblocking. The advantage of the algorithm over the solution available in the literature is that it does not involve iterations on the supremal controllable sublanguage and supremal normal sublanguage operators.     

Null controllability of the Burgers system with distributed controls

This paper is devoted to present some positive and negative controllability results for the viscous Burgers equation. More precisely, in the context of null controllability with distributed controls, we present sharp estimates of the minimal time of controllability T(r) of initial data of L²-norm less or equal to r. In particular, we see that (global) null controllability does not hold in general (unless the control is exerted everywhere). The same results apply to similar boundary controllability systems with one boundary control.     

A stabilization problem with respect to a target set for affine uncontrollable systems

The principal contribution of this paper is that it shows how much the controllability condition can be weakened, while still providing the possibility of stabilization. A result concerning stabilization with respect to a target set for affine control systems in the lack of the full rank condition is proved.