State analysis of linear time delayed systems via Haar wavelets. (English) Zbl 1017.65530
Summary: State analysis of time delayed systems via Haar wavelets are proposed in this paper. Based upon some useful properties of Haar functions, a special product matrix and a related coefficient matrix are applied to solve the time-delayed systems. The unknown Haar coefficient matrix is solved via the Kronecker product method. The high accuracy and the wide applicability of Haar approach will be demonstrated with numerical examples.
MSC:
| 65T60 | Numerical methods for wavelets |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
References:
| [1] | Chen, C. F.; Hsiao, C. H.: Haar wavelet method for solving lumped and distributed-parameter systems. IEE proc. Pt. D 144, 87-94 (1997) · Zbl 0880.93014 |
| [2] | Hsiao, C. H.; Hsiao, C. H.; Wang, W. J.: States analysis and parameters estimation of bilinear systems via Haar wavelets. IEEE trans. Circuits and systems-I: fundamental theory and applications (1996) |
| [3] | Hsiao, C. H.; Wang, W. J.: State analysis and optimal control of linear time-varying systems via Haar wavelets. IEE proc. Pt. D (1997) |
| [4] | Haar, A.: Zur theorie der orthogonalen funktionen systeme. Math. ann. 69, 331-371 (1910) · JFM 41.0469.03 |
| [5] | Karanam, V. R.; Frick, P. A.; Mohler, R. R.: Bilinear system identification by Walsh functions. IEEE trans. 23, No. 4, 709-713 (1978) · Zbl 0381.93018 |
| [6] | Chen, C. F.; Hsiao, C. H.: Time domain synthesis via Walsh functions. IEE proc. 122, 565-570 (1975) |
| [7] | Chen, C. F.; Hsiao, C. H.: Walsh series analysis in optimal control. Int. J. Control 21, No. 6, 881-897 (1975) · Zbl 0308.49035 |
| [8] | Chen, C. F.; Hsiao, C. H.: A state-space approach to Walsh series solution of linear systems. Int. J. Syst. sci. 6, No. 9, 833-858 (1975) · Zbl 0311.93015 |
| [9] | Chen, C. F.; Hsiao, C. H.: Design of piecewise constant gains for optimal control via Walsh functions. IEEE trans. 20, No. 5, 569-603 (1975) · Zbl 0317.49042 |
| [10] | Chen, W. L.; Shih, Y. P.: Shift Walsh matrix and delay-differential equations. IEEE trans. 23, No. 6, 1023-1028 (1978) · Zbl 0388.93029 |
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