Fundamental properties of the impulse response of low-order linear systems†

1969 ◽  
Vol 9 (2) ◽  
pp. 179-204 ◽  
Author(s):  
J. M. BROWN ◽  
J. D. LAMB
Keyword(s):  
Linear Systems ◽  
Impulse Response ◽  
Order Linear ◽  
Fundamental Properties ◽  
Low Order

‘Prediction of the Transient Response Sensitivity of High Order Linear Systems Using Low Order Models’

1970 ◽  
Vol 3 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
D. R. Towill ◽  
Z. Mehdi
Keyword(s):  
Linear Systems ◽  
Transient Response ◽  
High Order ◽  
Analogue Computer ◽  
Order Model ◽  
Analogue Model ◽  
Response Sensitivity ◽  
Order Linear ◽  
Accuracy Of Prediction ◽  
Low Order

It is shown that low order models can be used to predict adequately the transient response sensitivity of high order linear systems, thus leading to a great reduction in time and complexity during analogue or digital computation, as well as facilitating the understanding of the sensitivity functions themselves. Experimental results on an analogue model of a sixth order aircraft blind landing system confirm the adequacy of the procedure. In this instance the use of the low order model eliminates six integrators from the analysis and it is to be expected that higher order systems will lead to even greater savings. The example used to illustrate the procedure is the practical problem of setting parameter tolerances given acceptable bounds of transient performance. A new low order model is introduced, and when compared with alternative models proposed elsewhere in the literature is found to give an encouraging accuracy of prediction. The new model is particularly useful if the sensitivity analysis is undertaken on an analogue computer.

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

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