The linear-quadratic-Gaussian control design using an improved product formula of Walsh functions

By using the Walsh functions an approximate solution is obtained for the linear-quadratic-Gaussian control design problem. An improved formula of Walsh functions is derived for giving a simple expression of products of two or more arbitrary matrix time functions. It is shown that the Riccati matrix equation can directly be solved with the improved formula. Calculation results are presented to illustrate the validity and applicability of this method.