State analysis and optimal control of linear time-varying systems via Haarwavelets

State analysis and optimization of time-varying systems via Haar wavelets a re proposed in this paper. Based upon some useful properties of Haar functi ons, a special product matrix and a related coefficient matrix are applied to solve the time-varying systems first. Then the backward integration is i ntroduced to solve the adjoint equation of optimization. The unknown Haar c oefficient matrix will be in generalized Lyapunov equation form, which is s olved via a single-term algorithm. The local property of Haar wavelets is f ully applied to shorten the calculation process. A brief comparison between Haar wavelet and other orthogonal functions is also given. Copyright (C) 1 998 John Wiley & Sons, Ltd.