Van Loan’s expm formula for variance discretization in linear stochastic ODEs

Antonio Sala, UPV

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Abstract/Summary:

This material develops the particularization of Van Loan’s formulae (paper https://doi.org/10.1109/TAC.1978.1101743 ) to numerically compute, with a single matrix exponential, the integral of exponentials of matrices resulting from the solution of variance equations in linear processes subject to white noise.

The presented formula (or its dual transposed one) is used in Matlab’s commands kalmd and lqrd in discrete-time Kalman filter synthesis for LTI systems.