Controllability and observability for time‐varying switched impulsive controlled systems

This paper is concerned with the controllability and observability for linear time‐varying switched impulsive systems. First, some new results about the variation of parameters for time‐varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time‐varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.     

Necessary and sufficient conditions for controllability and observability of switched impulsive control systems

Many practical systems in physics, biology, engineering, and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This note first introduces the impulsive behavior into switched linear systems and studies the controllability and observability of such systems. Necessary and sufficient criteria for reachability and controllability are established. It is proved that reachability is equivalent to controllability for such systems. Then, necessary and sufficient criteria for observability and determinability of such systems are established by duality. It is also proved that observability is equivalent to determinability. Our criteria are of geometric type, they can be transformed into algebraic form conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.     

On controllability and observability of time delay systems

This paper deals with controllability and observability properties of time delay systems in the state spaceR^{n} times L^{p}. In particular, we prove the equivalence of spectral controllability and approximate null-controllability. Moreover, it is shown that the necessary, condition for approximateF-controllability-obtained recently by Manitius-is also sufficient, and a verifiable and matrix type criterion forF-controllability is derived for systems with commensurate delays. Finally, we introduce the dual observability notion of approximate controllability and prove that the control system Σ is exactly null-controllable if and only if the transposed delay system Σ^Tis continuously finally observable.     

Recursive controllability and observability tests for large dynamic systems

Controllability and observability criteria for a linear stationary system are used to design recursive tests for slackening the computing system requirements for verification of the controllability and observability of large systems. Practical examples are given.     

Structure analysis via orthogonal functions

The use of orthogonal functions to analyse the structure of a system is investigated. Applying the definitions of observability and controllability to a system that is approximated with the help of orthogonal functions, it is shown that the concepts of the state space and the space of orthogonal functions are equivalent, provided that two weak conditions are met. This result ensures that the observability and controllability properties remain invariant under the transformation introduced by the approximation. Furthermore, new criteria to test observability and controllability are given in terms of the coefficient matrix of the orthogonal expansion. Because this test does not require the knowledge of the system matrices A, B and C, the results derived may be used for the identification of systems. It is demonstrated that all the results obtained remain true, even for an approximation with low accuracy. These properties allow the application of orthogonal functions for the analysis of systems     

Band criteria and recursive tests of complete controllability and observability of linear algebraic-differentiable systems

New criteria are introduced of complex controllability and observability of controllable linear stationary algebraic-differentiable systems with many inputs and outputs, which reduce to the calculation of the rank of special band matrices. Recursive tests are set up, which permit reducing computational expenses in the verification for the fulfillment of the conditions of complete controllability and observability of algebraic-differentiable systems of a large dimension.     

CONTROLLABILITY OF A CLASS OF SINGULAR SYSTEMS

In this paper, several different concepts of controllability are investigated for a class of linear singular systems which system parameters are piecewise constant. Necessary and sufficient geometric criteria for C‐controllability and R‐controllability of such systems are established, respectively. These conditions can be easily transformed into algebraic form. By applying the principle of duality, C‐observability is discussed as well. Furthermore, the intrinsic relationship between these results and existing results are also discussed. Then, a novel necessary, and sufficient criterion for C‐controllability of linear time‐invariant singular systems is derived as a byproduct.     

网络控制系统的能控性和能观性

给出了网络控制系统的定义，并基于线性时不变系统的被控对象，建立了传感器为时钟驱动，控制器和作动器为事件驱动时长时滞网络控制系统的数学模型，对网络控制系统的均值能控、均方能控、均值能观及均方能观作了定义，得到了网络控制系统能控的充分或必要条件及能观的充要条件．     

广义动态系统的微分算子矩阵方法

本文用微分算子矩阵方法讨论了一类广义动态系统的结构性质,并且用微分算子多项式 矩阵的系数阵,给出了各类动态系统能控(观)性的直接判据.它是用微分算子矩阵方法研究 广义动态系统的开端.     

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

To control and observe spatially distributed thermal flow systems, the controllable field and observable field around the actuator and sensor are of interest, respectively. For spatially distributed systems, the classical systems theoretical concepts of controllability and observability are, in general, difficult to apply. In this study, sensitivity fields were used to analyse the behaviour from input to state and from initial state to output. For the analysis of controllability and observability, a large-scale, bulk storage facility with coupled thermal flow of air and agro-products was used. Analysis of this system using the classical systems theory results in controllability and observability results that are dependent on the step size of the spatially discretised system. Due to matrix multiplications, inaccurate results are calculated if the step size is too small. Our findings indicate that input-state and initial-state output sensitivity fields provide sufficient information about the controllability and observability of large coupled spatially distributed systems, using finite-dimensional state space representation with small discretisation steps.     

Observability and controllability analysis for sandwich systems with dead-zone

In this paper, an approach to analyze the observability and controllability of sandwich systems with dead-zone is proposed. In this method, a non-smooth state-space function is proposed to describe the sandwich systems with dead-zone which are also non-smooth nonlinear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium points that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with dead-zone are derived. Finally, a numerical example is presented.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.     

System theoretic properties of a class of spatially invariant systems

In this paper we develop new readily testable criteria for system theoretic properties such as stability, controllability, observability, stabilizability and detectability for a class of spatially invariant systems. Our approach uses the well-established theory developed to solve infinite-dimensional systems. The theoretical results are illustrated by several examples.     

Proper stable Bezout factorizations and feedback control of linear time-delay systems†

This paper deals with the existence and construction of proper stable Bezout factorizations of transfer function matrices of linear time-invariant systems with commensurate time delays. Existence of factorizations is characterized in terms of spectral controllability (or spectral observability)of the co-canonical (or canonical) realization of the transfer function matrix. An explicit procedure for computing proper stable Bezout factorizations is given in terms of a specialized ring of pure and distributed time delays. This procedure is utilized to construct finite-dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed-loop system.     

Robustness of controllability and observability of continuouslinear time-varying systems with parameter perturbations

The controllability and the observability of continuous linear time-varying systems with norm-bounded parameter perturbations are analyzed. The sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system. The proposed sufficient conditions allow the evaluation of controllability under the norm-bounded parameter perturbations. The robustness of the observability is also studied for continuous linear time varying systems with norm-bounded parameter perturbations, and the corresponding sufficient conditions are provided     

线性时变广义系统的能控性与能观性问题

讨论了线性时变系统和线性时变广义系统的两个基本问题, 得到了两种判定时变系统能控性与能观性的必要条件, 该判定条件只依赖于系统矩阵A(t)和输入矩阵B(t), 不必计算系统的系统状态转移矩阵, 使得判别时变系统能控性与能观性易于实现. 说明了本文结论是线性定常系统相应结论的自然扩展. 对进一步深入研究时变系统和时变广义系统具有实际启发作用.     

The robustness of controllability and observability for discrete linear time-varying systems with norm-bounded uncertainty

Controllability and observability of discrete linear time-varying systems with norm-bounded parameter uncertainties are analyzed in this note. Like in the continuous case, we propose the sufficient conditions, which ensure controllability and observability of the uncertain system. The proposed conditions allow the evaluation of controllability and observability of the uncertain system without knowledge of specific values of uncertainties.     

Duality theorems on control and observation of discrete-time infinite-dimensional systems

General discrete-time infinite-dimensional linear systems in normed spaces are considered. controllability and observability properties related to the problem of feedback stabilization are examined. Special emphasis is put on deriving duality theorems, that is, for a given controllability concept an equivalent observability concept for the dual observed system is found. Finite-time as well as infinite-time cases are considered.     

New necessary and sufficient conditions for local controllability and local observability of 2-D separable denominator systems

New necessary and sufficient conditions for local controllability and observability of 2-D separable denominator systems (SDS's) are presented on the basis of the reduced-dimensional decomposition of 2-D SDS's. It is proved that local controllability of a 2-D SDS is equivalent to controllability of two 1-D systems which are a special decomposition pair of the 2-D SDS. Furthermore, local observability of a 2-D SDS is equivalent to a full rank condition of the coefficient matrices of the 2-D SDS in addition to observability of two 1-D systems which are another special decomposition pair of the 2-D SDS. Thus, these new conditions which use only 1-D controllability matrices, 1-D observability matrices, and coefficient matrices of the 2-D SDS are much simpler than any previous conditions which use complex 2-D controllability and observability matrices.     

2-D系统模能控性和模能观性判据

本文指出并纠正了文［１～３］关于２－Ｄ系统模能控性和模能观性判据的错误。