q-Difference linear control systems

We propose q-difference versions of some basic results of complete controllability and observability of linear systems such as criterions of controllability and observability, controllability and observability canonical forms, the q-duality theorem, the interconnection between these concepts and that of polynomials without common zeros. As an appendix, is given a simple but computationally meaningful Maple Procedure for the controllability criterion for time constant systems.     

Controllability and observability of coordinated linear systems

This paper develops concepts of controllability and observability for the class of coordinated linear systems, a special class of linear hierarchical systems with a top-to-bottom information structure. The usual concepts of reachability and indistinguishability for linear systems are refined, taking into account the decentralized nature of coordinated linear systems. The corresponding controllability and observability decompositions are derived, and several concepts of controllability and observability for coordinated linear systems are introduced and discussed. These results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems.     

Controllability and Observability of Linear Quaternion-valued Systems

The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.     

DUALITY IN LINEAR CONTROL SYSTEMS

The present paper establishes various duality relations-equalities which exist in linear control systems. By means of these relations, we demonstrate various duality properties in the theory of linear control systems. In particular we discuss the duality of controllability and observability of linear systems, the concepts of controllability and observability in stochastic systems the duality of regulator and observer of time-invariant systems and the duality property of reduced dimension observers etc. The duality relation established here is used to solve the problem of min-max state estimation in systems with uncertainty.     

Controllability and observability for a class of time-varying impulsive systems

This paper is concerned with the controllability and observability for a class of piecewise linear time-varying impulsive systems. Several sufficient and necessary conditions for state controllability and observability of such systems are established. Meanwhile, corresponding criteria for time-invariant impulsive systems are also obtained and the criteria are compared with the existing results.     

Controllability and observability of a class of linear impulsive systems

This paper studies the controllability and observability of a class of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of geometric type, they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.     

Controllability and observability for impulsive systems in complex fields

Since the classical example of complex system is the quantum system which is one of the foci of ongoing research, in this paper, the issue of controllability and observability for a class of time-varying impulsive systems defined in complex fields, to be brief, complex time-varying impulsive systems, is addressed. Several sufficient and necessary conditions for state controllability and observability of such systems are established. Meanwhile, corresponding criteria for complex linear time-invariant impulsive systems are also obtained.     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

Observability of hybrid discrete-continuous systems

We study the statement and solvability of observability problems in linear stationary hybrid discrete-continuous dynamical systems. Necessary and sufficient observability conditions expressed directly via the system parameters are derived. We consider linear observability problems and the dual controllability and reachability problems. The problem of computing the minimum number of inputs for which the system has a given observability is discussed. An example illustrating the results is presented.     

On constraint controllability of linear systems in Banach spaces

In this paper, we give an addendum to a result of Dolecki and Russell (Ref. 1) related to the duality relationship between observation and control for linear systems in Banach spaces. Our results relate the controllability of a system to the constraint controllability of that system and to the observability of an adjoint system. The main tool used here is an extension of the classical open mapping theorem.     

CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF FRACTIONAL-ORDER IMPULSIVE SYSTEMS

This paper studies the controllability and observability for a class of fractionalorder impulsive systems.First,the basic acknowledgement of fractional-order systems is presented.Then the solution of the fractional-order impulsive systems is given.Finally,necessary and sufficient criteria for controllability and observability are obtained.     

Controlled and conditioned invariant subspaces in linear system theory

The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.     

How to define the dual of a higher-dimensional linear system

The classical duality of linear systems is generalized to higher dimensions. Consequently, a new insight is given to the concepts of controllability and observability, and autonomy.     

组合系统的行为化方法

在行为框架下研究线性微分组合系统的建模问题 .建立了 n个子系统串、并联组合系统的行为化模型 ,给出了其能控性、能观性的判别条件 .分析过程表明用行为化方法对组合系统的研究有着比传统方法更便捷、适用的模型类更广等优点 .     

Duality in controllability and observability problems for nonstationary hybrid impulsive differential-difference systems

We consider linear nonstationary hybrid differential-difference dynamical observable systems under the action of impulses, which generates jumps in the corresponding solutions of the systems. For such systems, we construct dual controllability problems and prove a general duality relation, which permits one to state a general duality principle in controllability and observability problems for hybrid differential-difference systems. The results are illustrated by an example.     

广义区间系统可控和可观测的充分条件

分别给出了单输入多输出广义区间系统可控和多输入单输出广义区间系统可观测的充分条件     

分布参数系统能控能观性问题的统一处理及应用

本文的主要目的是介绍一个统一的处理分布参数系统能控能观性问题的方法,并给出该方法在分布参数控制理论中的应用。为此,本文将从一类“类抛物” 偏微分算子（即没有椭圆性条件）的带权恒等式出发,给出所有已知的关于抛物型方程、双曲型方程、Schrödinger 方程和板方程的基于整体Carleman 估计的能控能观性结果。同时,基于该带权的恒等式,本文还给出它在双曲型系统的稳定性问题和在拟线性复Ginzburg-Landau 方程能控能观性等问题中的应用。     

Persistent regional null controllability of some degenerate wave equations

This paper is addressed to a study of the persistent regional null controllability problems for one‐dimensional linear degenerate wave equations through a distributed controller. Different from non‐degenerate wave equations, the classical null controllability results do not hold for some degenerate wave equations. Thus, persistent regional null controllability is introduced, which means finding a control such that the corresponding state of the degenerate wave equation may vanish in a suitable subset of the space domain in a period of time. In order to solve this problem, we need to establish the regional null controllability for degenerate wave equations. This problem is reduced to a suitable observability problem of a linear degenerate wave equation. The key point is to choose a suitable multiplier in order to establish this observability inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — The Constructive Method*

In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary (null) controllability and the exact boundary observability for first order hyperbolic systems.     

Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — the HUM Method*

The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work [Lu, X. and Li, T. T., Exact boundary controllability of weak solutions for a kind of first order hyperbolic system — the constructive method, Chin. Ann. Math. Ser. B, 42(5), 2021, 643–676]. In this paper, in order to study these problems from the viewpoint of duality, the authors establish ...