Journal ArticleDOI
Observing the State of a Linear System
TLDR
In this article, it was shown that the state vector of a linear system can be reconstructed from observations of the system inputs and outputs, and that the observer which reconstructs this state vector is itself a linear systems whose complexity decreases as the number of output quantities available increases.Abstract:
In much of modern control theory designs are based on the assumption that the state vector of the system to be controlled is available for measurement. In many practical situations only a few output quantities are available. Application of theories which assume that the state vector is known is severely limited in these cases. In this paper it is shown that the state vector of a linear system can be reconstructed from observations of the system inputs and outputs. It is shown that the observer, which reconstructs the state vector, is itself a linear system whose complexity decreases as the number of output quantities available increases. The observer may be incorporated in the control of a system which does not have its state vector available for measurement. The observer supplies the state vector, but at the expense of adding poles to the over-all system.read more
Citations
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Journal ArticleDOI
An introduction to observers
TL;DR: In this paper, the identity observer, a reduced-order observer, linear functional observers, stability properties, and dual observers are discussed, along with the special topics of identity observer and reduced order observer.
Journal ArticleDOI
Observers for multivariable systems
TL;DR: In this article, it was shown that the design of an observer for a system with M outputs can be reduced to the design for m separate observers for single-output subsystems.
Journal ArticleDOI
Adaptive observers with exponential rate of convergence
TL;DR: In this article, the problem of observing the state of an unknown, time invariant linear system from measurements of its input and output is considered, and the approach taken here proceeds from a parametrized observer, which is only an alternative, equivalent representation of the Luenberger observer.
Book
Controlled and conditioned invariants in linear system theory
Giuseppe Basile,Giovanni Marro +1 more
TL;DR: In this paper, general properties of linear systems are discussed, and the geometric approach -analysis, synthesis, robustness optimality, and robustness optimization -are presented, respectively.
Journal ArticleDOI
Control Principles of Complex Networks
TL;DR: Recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components.
References
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Journal ArticleDOI
New Results in Linear Filtering and Prediction Theory
R. E. Kalman,R. S. Bucy +1 more
TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Journal ArticleDOI
Mathematical description of linear dynamical systems
TL;DR: In this paper, it is shown that the input/output relations determine only one part of a system, that which is completely observable and completely controllable, and methods are given for calculating irreducible realization of a given impulse-response matrix.
Journal ArticleDOI
On the general theory of control systems
TL;DR: In this paper, a general theory of control systems is outlined which answers many basic questions (what is controllable? why? how?) and gives a highly efficient method of computation.