Journal ArticleDOI
Optimal minimal-order observer-estimators for discrete linear time-varying systems
E. Tse,Michael Athans +1 more
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In this paper, the authors generalize and unify the concepts developed by Kalman and Luenberger pertaining to the design of discrete linear systems which estimate the state of a linear plant on the basis of both noise-free and noisy measurements of the output variables.Abstract:
This paper generalizes and unifies the concepts developed by Kalman and Luenberger pertaining to the design of discrete linear systems which estimate the state of a linear plant on the basis of both noise-free and noisy measurements of the output variables. Classes of minimal-order optimum "observer-estimators" are obtained which yield the conditional mean estimate of the state of the dynamical system. One explicit minimal-order optimal observer-estimator is constructed which generates one version of the conditional mean state estimate.read more
Citations
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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 nonlinear stochastic systems
Tzyh-Jong Tarn,Y. Rasis +1 more
TL;DR: In this article, sufficient conditions on the structure of a nonlinear stochastic system for the existence of an exponentially bounded observer are given, and sufficient conditions to stabilize cascaded control and observer in a feedback arrangement are given.
Journal ArticleDOI
Optimal limited state variable feedback controllers for linear systems
TL;DR: In this article, the problem of designing compensators, the dimensions of which are fixed a priori, for linear systems is considered, and two types of compensators are considered: static (gain only) compensators which operate directly upon the output signals to generate the controls, and dynamic compensators of fixed dimension.
Journal ArticleDOI
Recursive discrete Fourier transformation
TL;DR: In this paper, the authors present new discrete Fourier transform methods which are recursive, expressible in state variable form, and involve real number computations, which are especially useful for running Fourier transformation and for general and multirate sampling.
Journal ArticleDOI
Structure determination and parameter identification for multivariable stochastic linear systems
Edison Tse,Howard L. Weinert +1 more
TL;DR: In this article, the problem of using output data to identify a constant, multivariable, stochastic linear system which has unknown dimension, system matrices, and noise covariances is considered.
References
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A Generalized inverse for matrices
TL;DR: A generalization of the inverse of a non-singular matrix is described in this paper as the unique solution of a certain set of equations, which is used here for solving linear matrix equations, and for finding an expression for the principal idempotent elements of a matrix.
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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.
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Observing the State of a Linear System
TL;DR: 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.
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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.