Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems
01 Jan 1981-Siam Journal on Control and Optimization (Society for Industrial and Applied Mathematics)-Vol. 19, Iss: 1, pp 20-32
TL;DR: In this article, the concepts of detectability and stabilizability are explored for time-varying systems, including invariance under feedback, an extended version of the lemma of Lyapunov, existence of stabilizing feedback laws, linear quadratic filtering and control, and the existence of approximate canonical forms.
Abstract: The concepts of detectability and stabilizability are explored for time-varying systems. We study duality, invariance under feedback, an extended version of the lemma of Lyapunov, existence of stabilizing feedback laws, linear quadratic filtering and control, and the existence of approximate canonical forms.
Citations
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TL;DR: It is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough.
Abstract: The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.
867 citations
TL;DR: In this paper, the problems of filtering and smoothing are considered for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are otherwise arbitrary.
Abstract: The problems of filtering and smoothing are considered for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered; the initial condition is assumed known in one case, while in the other the initial condition is not known but the initial condition, the plant, and measurement noise are in some weighted ball of R/sup n/XL/sub 2/. Finite-horizon and infinite-horizon cases are considered. Necessary and sufficient conditions are presented for the existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, and algorithms that result in performance within the bounds are developed. In case of smoothers, the optimal smoother is also presented. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which both linear time-varying and time-invariant systems can be considered with equal ease. (In the smoothing problem, for linear time-varying systems, one considers only the finite-horizon case). >
835 citations
TL;DR: The topic of synchronization of the response of systems has received considerable attention and this concept is revisited in the light of the classical notion of observers from (non)linear control theory.
Abstract: In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory,.
716 citations
Additional excerpts
...We refer the interested reader to [20]....
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01 Jan 1993
TL;DR: A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques.
Abstract: A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques. Both known and new SVD-based identification methods are classified in a subspace-oriented scheme. The SVD of a matrix constructed from the observed signal data provides the key step in a robust discrimination between desired signals and disturbing signals in terms of signal and noise subspaces. The methods that are presented are distinguished by the way in which the subspaces are determined and how the signal or system model parameters are extracted from these subspaces. Typical examples, such as the direction-of-arrival problem and system identification from input/output measurements, are elaborated upon, and some extensions to time-varying systems are given. >
344 citations
TL;DR: In this article, a modified gain extended Kalman observer (MGEKO) was developed for a special class of systems and a sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square was obtained.
Abstract: A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.
287 citations