Comments on "The maximally achievable accuracy of linear optimal regulators and linear optimal filters"

Godbole, S.

doi:10.1109/tac.1972.1100021

Cited by 11 publications

(2 citation statements)

References 5 publications

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“…Remark 5.4. As is pointed out by Godbole [6], the condition of theorem 3.1 corresponds to the requirement that the model is invertible and that the inverse has no unstable modes (in the sense of linear systems). Indeed, note that H(λI − A) −1 D is the transfer function associated to our filtering model, so that invertibility holds in this setting if and only if the matrix H(λI − A) −1 D has a left inverse for all but a finite number of λ ∈ C (see, e.g., [14, theorem 5]).…”

Section: Linear Gaussian Modelsmentioning

confidence: 99%

When Do Nonlinear Filters Achieve Maximal Accuracy?

Handel¹

2010

SIAM J. Control Optim.

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The nonlinear filter for an ergodic signal observed in white noise is said to achieve maximal accuracy if the stationary filtering error vanishes as the signal to noise ratio diverges. We give a general characterization of the maximal accuracy property in terms of various systems theoretic notions. When the signal state space is a finite set explicit necessary and sufficient conditions are obtained, while the linear Gaussian case reduces to a classic result of .

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Section: Linear Gaussian Modelsmentioning

confidence: 99%

When Do Nonlinear Filters Achieve Maximal Accuracy?

Handel¹

2010

SIAM J. Control Optim.

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“…To prove sufficiency it is initially observed that conditions (36) imply that (A2, B2) is stabilizable from Lemma 1. Assume now that C2 # 0, where C2 is defined by (11). Then it follows from the definition of Ht that where T2, an orthogonal matrix, is given by (1 I), and Ai, B2 are given by (23).…”

Section: (34)mentioning

confidence: 99%

The optimal LQ regulator with cheap control for not strictly proper systems

Scherzinger

Davison

1983

The 22nd IEEE Conference on Decision and Control

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SUMMARYThe LQ optimal regulator problem with cheap control is investigated for plants of the form i = Ax + Bu, y = Cx + Du, where D # 0 makes the plant not strictly proper. It is found that perfect regulation of the output with closed-loop stability is achieved if and only if the plant is detectable, is minimum phase and there exist independent inputs equal to or greater in number to the number of independent outputs.

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The optimal LQ regulator with cheap control for not strictly proper systems

Scherzinger

Davison

1985

Optim Control Appl Methods

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The LQ optimal regulator problem with cheap control is investigated for plants of the form x = Ax + Bu, y = Cx + Du, where D ± 0 makes the plant not strictly proper. It is found that perfect regulation of the output with closed‐loop stability is achieved if and only if the plant is detectable, is minimum phase and there exist independent inputs equal to or greater in number to the number of independent outputs.

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Comments on "The maximally achievable accuracy of linear optimal regulators and linear optimal filters"

Cited by 11 publications

References 5 publications

When Do Nonlinear Filters Achieve Maximal Accuracy?

When Do Nonlinear Filters Achieve Maximal Accuracy?

The optimal LQ regulator with cheap control for not strictly proper systems

The optimal LQ regulator with cheap control for not strictly proper systems

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