State Analysis of Time-invariant Singular Systems via Haar Wavelets

Singular systems have been the subject of interest over the last two decades due to their many practical applications. On the other hand, there has been considerable interest in the application of various orthogonal functions such as Walsh, block pulse, Hermite and recently wavelets family in signal processing due to their great properties to approximate signals. This paper proposed a numerical method for analyzing time-invariant singular systems via Haar wavelets. Based upon some properties of Haar wavelets a special operational matrix of integration is applied to the time-invariant singular systems such that the state equation of these systems can be solved easily. In addition, a necessary and sufficient condition for existence of the solution for these systems with Haar wavelets approach will be given. Results clearly demonstrates the advantages of the Harr wavelets approach.