Observability conservation by output feedback and observability Gramian bounds

Zhang, Liangquan; Zhang, Qinghua

doi:10.1016/j.automatica.2015.06.031

Cited by 13 publications

(14 citation statements)

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“…The continuous time counterpart of this result is known as part of the lemma on observability conservation by output feedback (Anderson et al, 1986;Sastry and Bodson, 1989;Ioannou and Sun, 1996;Zhang and Zhang, 2015). However, for discrete time systems, this result seems not reported in the literature.…”

Section: Stability Of the Kalman Predictormentioning

confidence: 67%

On stability of the Kalman filter for discrete time output error systems

Zhang

2017

Systems & Control Letters

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The stability of the Kalman filter is classically ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. This paper studies the case of discrete time output error (OE) systems, in which the process noise is totally absent. The classical stability analysis assuming the controllability regarding the process noise is thus not applicable. It is shown in this paper that the uniform complete observability is sufficient to ensure the stability of the Kalman filter applied to time varying OE systems, regardless of the stability of the OE systems. Though the continuous time case has been studied recently, the results on continuous time systems cannot be directly transposed to discrete time systems, because of a difficulty related to the observability of the discrete time filter error dynamics system.

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Section: Stability Of the Kalman Predictormentioning

confidence: 67%

On stability of the Kalman filter for discrete time output error systems

Zhang

2017

Systems & Control Letters

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“…Remark Clearly, the prime stochastic linear system () has been transformed into a deterministic system. Therefore, we are able to use the classical observability Gramian, and then the results shown in Zhang and Zhang [5] will be employed. The key point here is to re‐estimate the bounds since the appearance of diffusion term (see Theorem 3.1 below).…”

Section: Resultsmentioning

confidence: 99%

H‐representation to stochastic observability conservation by output feedback and Gramian bounds

Zhang,

Zhang

2023

Asian Journal of Control

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In this paper, we are concerned with uniform complete observability of linear stochastic time‐varying systems conserved by output feedback and Gramian bounds via so called ‐representation method. We obtain the lower and upper bounds for the Gramian of output feedback stochastic system from the original system and vice versa. A numerical example is constructed to verify the effectiveness of our main result. The uniform complete observability is useful for the analysis and synthesis of the Kalman filter.

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“…The proof for a slightly different lemma can be found in (Zhang, 2017), with a UCO definition equivalent to that of (Jazwinski, 1970), but different from (Moore and Anderson, 1980). Some related results for continuous time systems are available in (Sastry and Bodson, 1989;Ioannou and Sun, 1996;Zhang and Zhang, 2015).…”

Section: Auxiliary Resultsmentioning

confidence: 99%

Stability analysis of the Kalman predictor

Zhang

2019

International Journal of Control

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The stability of the Kalman filter, though less often mentioned than the optimality in the recent literature, is a crucial property for real time applications. The purpose of this paper is to complete the classical stability analysis of the Kalman filter for general time varying systems. A proof of the stability of the one step ahead predictor, which is embedded in the Kalman filter, is presented in this paper, whereas the classical results were focused on the stability of the filter. The predictor stability is particularly important for linear parameter varying (LPV) system identification by means of prediction error minimization.

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Observability conservation by output feedback and observability Gramian bounds

Cited by 13 publications

References 1 publication

On stability of the Kalman filter for discrete time output error systems

On stability of the Kalman filter for discrete time output error systems

H‐representation to stochastic observability conservation by output feedback and Gramian bounds

Stability analysis of the Kalman predictor

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