Chapter 1: Invited Addresses and Tutorials on Signals, Coding,
  Systems and Intelligent Techniques

Title: Analysis of Singular Systems using the Haar Wavelet Transform

Author(s): Dimitrios A. Karras, Panagiotis Sotiropoulos, Basil G. Mertzios

Address: Department of Automation, Chalkis Institute of Technology, and Hellenic Open University, Psachna, 34400, Evoia, Greece University of the Aegean, 83200, Karlovassi, Samos, Greece | Educational Technology Laboratory, Cultural and Educational Technology Institute (CETI) Centre of Integrated Research for the Information Society (I.R.I.S.). 58 Tsimiski Street, 67100 Xanthi, Greece | Department of Automation, Laboratory of Control Systems and Comp. Intell. Thessaloniki Institute of Technology, Thessaloniki, Greece

Reference: 12th International Workshop on Systems, Signals and Image Processing pp. 195 - 198

Abstract/Summary: In this paper the application of Haar wavelets is investigated in the problem of determining the trajectory sensitivity function of singular systems. It is shown that the corresponding differential-algebraic system equation could be converted to an algebraic generalized Lyapunov equation that could be solved for the coefficients of the state variables in terms of the Haar wavelet basis, This paper extends the results of Lewis F.L. and Mertzios B.G. (1987), in the problem of trajectory sensitivity analysis of singular systems as well as the results of Chen C. F. and Hsiao C. H (1997) in the application of Haar wavelets in singular systems analysis. The solution of the generalized Lyapunov equation is based on the generalization of the Bartels/ Stewart algorithm as discussed in Lewis F.L. and Mertzios B.G. (1987).

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