Abstract
Abstract Extension of Walsh functions to the analysis of time-varying linear systems is made by the introduction of the product matrix of Walsh vector and its transpose, and the operational property of product matrix. The operational matrix for the backward integration of Walsh functions is first introduced. Therefore, the state transition matrix of optimal control of linear time-varying systems with quadratic performance index can be integrated approximately using Walsh functions. The solution of the state transition matrix leads to piecewise constant gains equally distributed.
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