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A note on the evaluation of the total integral for continuous systems

This correspondence discusses a method of evaluation of a type of total integral that arises in the solution of asymmetric Lyapunov equations. The method of evaluation is based on an earlier work by Jury and Dewey (1965). Analytical solution of such equations is extremely useful for a practicing engineer who is interested in obtaining steady state solution for cross-covariance in the problem of track-to-track fusion with dissimilar sensors.