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.     

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 Controllability and Observability Tests

New controllability and observability tests for linear stationary dynamic systems are derived in the form of special banded matrices. Band tests aid in determining the conditionality of rank controllability and observability tests.     

关于区间矩阵稳定性、可控性、可观性的充要条件的注记

该文是对区间矩阵稳定性、可观性及可控性的充要条件的若干注记,给出其饼算子U的明确定义以及一个大区间矩阵分解成若干个子矩阵之饼的具体表达式.并进一步说明一个区间矩阵(无穷多个矩阵)的稳定性、可控性、可观性等价于该区间矩阵中的有限个矩阵的相应性质.建议了寻找这有限个矩阵的计算方法和步骤.     

On the controllability and observability of discrete-time linear time-delay systems

This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.     

Minimality and local state decompositions of a nonlinear state space realization using energy functions

In this paper a set of sufficient conditions is developed in terms of controllability and observability functions under which a given state-space realization of a formal power series is minimal. Specifically, it is shown that positivity of these functions, in addition to a stability requirement and a few technical conditions, implies minimality. Using the nonlinear analogue of the Kalman decomposition, connections are then established between minimality, singular value functions, balanced realizations, and various notions of reachability and observability for nonlinear systems.     

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

非线性控制系统与状态空间的几何结构

首行从整体化的观点定义了一种建立在黎曼流形上的非线性控制系统,给出了系统的状态方程在黎曼流形的局部坐标系下的表达式,讨论了黎曼流形的几何结构对非线性系统的影响,研究了非线性系统的能控性和能观测性,其次,利用对合分布与全测地子流形的性质,给出了建立在黎曼流形上的非线性系统的局部能控结构分解,局部能观结构分解和Kalman分解,第三,分别利用彼此正交的对合分布族和递增对合分布族与全测地子流形族的性质。研究了建立在黎曼流形上的非线性控制系统平等解耦问题和级联解耦问题,以及仿射非线性控制系统的局部干扰解耦问题。     

Controllability and observability of linear time-invariant compartmental models

The problems of complete controllability and complete observability of linear time-invariant compartmental models with general input-output structures are considered. The analysis of these problems is based largely on graph-theoretic methods and the properties of polynomial matrices. Specifically, statements on complete controllability and complete observability are proven by using graphical constructions which do not change the basic properties of controllability and observability. The major results of this paper are: 1) A unique decomposition of the digraph of a compartmental model into sources, sinks, and transits. 2) A theorem which states that a compartmental model with closed sinks is completely observable if and only if the matrix [C^{T}, A^{T}] is full rank, and a corollary which provides a sufficient condition for complete observability of all other linear time-invariant compartmental models. 3) A theorem which states that a single sink compartmental model is completely controllable if and only if a compartment from each source is controlled. 4) A controllability algorithm which provides sets of excitations which are sufficient for complete controllability of any linear time-invariant compartmental model.     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

On stabilizing receding horizon controls for linear continuoustime-invariant systems

In this paper, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-invariant systems under which nonincreasing or nondecreasing monotonicities of the optimal cost are guaranteed. It is shown that the proposed terminal inequality conditions guarantee the closed-loop stability of the receding horizon control with additional conditions of observability or controllability. The proposed terminal inequality conditions for the cost monotonicity and the closed-loop stability include most well-known existing terminal conditions as special cases     

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.     

Observability Conditions by Polynomial Ideals

In this paper, we give global and local observability conditions of polynomial systems. Each observability is defined in terms of distinguishability of a pair of initial states. The set of pairs of initial states are represented as an affine variety. By using this affine variety, a global observability condition is derived. Then, a local observability condition is presented based on the minimal decomposition of the affine variety and dimension theory.     

Span-reachability and observability of bilinear hybrid systems

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics are determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and span-reachability in terms of rank conditions for generalized observability and controllability matrices. This characterization is useful for the system theory of bilinear hybrid systems, in particular, it is used in the realization theory of bilinear hybrid systems, (Petreczky, 2006).     

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。     

Primeness of multivariate polynomial matrices

Different characterizations of primeness of polynomial matrices that are mutually equivalent in the one-dimensional case of univiriate polynomials lead to various primeness concepts in the multivariate situation. Applied to systems theory, this fact gives rise to a more refined view to observability and controllability of multidimensional systems. Algorithms for testing primeness properties are given based on computer algebraic techniques.     

Controllability, observability, and parameter identification of two coupled spin 1's

In this note, we study the control theoretic properties of a couple of interacting spin 1's driven by an electromagnetic field. In particular, we assume that it is possible to observe the expectation value of the total magnetization and we study controllability, observability, and parameter identification of these systems. We give conditions for controllability and observability and characterize the classes of equivalent models which have the same input-output behavior. The analysis is motivated by the recent interest in three level systems in quantum information theory and quantum cryptography as well as by the problem of modeling molecular magnets as spin networks.     

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.     

用多元有理函数矩阵研究系统的结构性质

本文着重介绍了各种结构化矩阵，经比较，说明多元有理函数矩阵（ＲＦＭ）能起初地描述线性物理系统，通过对多元有理函数域Ｆ（ｚ）上的能控制能观性的讨论，说明ＲＦＭ是研究与系统结构相关性质的有力工具，也说明了研究Ｆ（ｚ）上能控制观性的必要性。