scholarly journals The Structure of Autocovariance Matrix of Discrete Time Subfractional Brownian Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Guo Jiang
Keyword(s):  
Brownian Motion ◽  
Discrete Time ◽  
Approximation Theorem ◽  
Finite Impulse Response ◽  
Structure Theorem ◽  
Stationary Processes ◽  
Time Varying ◽  
Subfractional Brownian Motion ◽  
Autocovariance Matrix ◽  
Impulse Response Filter

This article explores the structure of autocovariance matrix of discrete time subfractional Brownian motion and obtains an approximation theorem and a structure theorem to the autocovariance matrix of this stochastic process. Moreover, we give an expression to the unique time varying eigenvalue of the autocovariance matrix in asymptotic means and prove that the increments of subfractional Brownian motion are asymptotic stationary processes. At last, we illustrate these results with numerical experiments and give some probable applications in finite impulse response filter.

Fault estimation of linear discrete time-varying systems with multiplicative noise based on finite impulse response filter

2019 ◽  
Vol 42 (3) ◽  
pp. 461-471 ◽  
Author(s):  
Yutao Wu ◽  
Shuai Liu ◽  
Yueyang Li ◽  
Zhonghua Wang
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Performance Index ◽  
Multiplicative Noise ◽  
Finite Impulse Response ◽  
Estimation Error ◽  
Estimation Accuracy ◽  
Fault Estimation ◽  
Time Varying ◽  
Time Varying Systems

This paper aims to construct a finite impulse response (FIR) based fault estimator for a class of linear discrete time-varying systems (LDTV) with multiplicative noise. Drawing support of intensive stochastic analyses and matrix manipulations, a novel performance index is proposed such that the fault estimation error is minimized in stochastic sense. A necessary and sufficient condition is established to guarantee the existence of the FIR-based fault estimator with satisfied estimation accuracy. The optimal gain of the desired fault estimator is calculated in an analytical way by minimizing the aforementioned performance index. Several examples are presented to demonstrate the effectiveness and superiority of the proposed methods.

A Simplified Method for Discrete-Time Repetitive Control Using Model-Less Finite Impulse Response Filter Inversion

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Yik R. Teo ◽  
Andrew J. Fleming ◽  
Arnfinn A. Eielsen ◽  
J. Tommy Gravdahl
Keyword(s):  
Discrete Time ◽  
Best Practice ◽  
Finite Impulse Response ◽  
Repetitive Control ◽  
Periodic Signal ◽  
Signal Model ◽  
Consistent Manner ◽  
Practice Methods ◽  
Impulse Response Filter ◽  
Selection Of

Repetitive control (RC) achieves tracking and rejection of periodic exogenous signals by incorporating a model of a periodic signal in the feedback path. To improve the performance, an inverse plant response filter (IPRF) is used. To improve robustness, the periodic signal model is bandwidth-limited. This limitation is largely dependent on the accuracy of the IPRF. A new method is presented for synthesizing the IPRF for discrete-time RC. The method produces filters in a simpler and more consistent manner than existing best-practice methods available in the literature, as the only variable involved is the selection of a windowing function. It is also more efficient in terms of memory and computational complexity than existing methods. Experimental results for a nanopositioning stage show that the proposed method yields the same or better tracking performance compared to existing methods.

Krein Space-based Hθ Fault Estimation for Linear Discrete Time-varying Systems

2009 ◽  
Vol 34 (12) ◽  
pp. 1529-1533 ◽  
Author(s):  
Mai-Ying ZHONG ◽  
Shuai LIU ◽  
Hui-Hong ZHAO
Keyword(s):  
Discrete Time ◽  
Krein Space ◽  
Fault Estimation ◽  
Time Varying ◽  
Time Varying Systems ◽  
Kreĭn Space
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