State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets |
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| Authors: | Hsiao C. H. Wang W. J. |
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| Affiliation: | (1) Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, Republic of China;(2) Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, Republic of China |
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| Abstract: | The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures. |
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| Keywords: | Optimal control discrete systems Haar wavelets |
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