Journal ArticleDOI
Solvability, controllability and observability of singular systems
TLDR
In this article, the problems of solvability, controllability, and observability for the singular system Kx(t)=Ax(t)+Bu(t), where K is a singular, square matrix andu(t) is a complex vector function sufficiently differentiable, are studied.Abstract:
The problems of solvability, controllability, and observability for the singular systemKx(t)=Ax(t)+Bu(t) are studied, whereK is a singular, square matrix andu(t) is a complex vector function sufficiently differentiable. The classical theories of matrix pencils are first related to the solvability of singular systems. Then, the concepts of reachability, controllability, and observability of regular systems are extended to singular systems. Finally, the set of reachable states is described. The proposed matrix conditions for testing the controllability and observability of singular systems are simple and always feasible.read more
Citations
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Book ChapterDOI
Controllability of Linear Differential-Algebraic Systems—A Survey
Thomas Berger,Timo Reis +1 more
TL;DR: In this article, different concepts related to controllability of differential-algebraic equations are described and defined in the time domain and equivalent criteria that generalize the Hautus test are presented and proved.
Journal ArticleDOI
Duality, observability, and controllability for linear time-varying descriptor systems
TL;DR: In this article, a characterization of observability and controllability for linear time-varying descriptor systems was developed. But observability of the original system is not equivalent to controllable control of the dual system, and neither E nor C were required to have constant rank.
Dissertation
On differential-algebraic control systems
TL;DR: In this paper, a differential algebraic equation (DAE) is defined as a set of differential-algebraic equations, in which the system is composed of two components, i.e., a system and a null dynamik.
Book ChapterDOI
Observability of Linear Differential-Algebraic Systems: A Survey
TL;DR: In this paper, different concepts related to observability of linear constant coefficient differential-algebraic equations are defined in the time domain and a normal form under output injection, state space and output space transformation is exploited to derive Hautus-type criteria for observability.
Journal ArticleDOI
On Kalman's controllability and observability criteria for singular systems
TL;DR: In this article, the controllability and observability properties of a singular system are investigated via rank criteria related to the Markov parameters from the inputs to the states and from the initial conditions to the outputs.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
Linear Multivariable Control: A Geometric Approach
TL;DR: In this article, the authors present an approach to controlability, feedback assignment, and pole shifting in a single linear functional model, where the observer is assumed to be a dynamic observer.
Journal ArticleDOI
A generalized state-space for singular systems
TL;DR: In this article, a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed, and concepts of controllability and observability are defined for the impulsive modes.