Modal decomposition constructs a similarity transformation for a linear system where the resulting coefficient matrix is a block diagonal structure corresponding to the real and complex eigenvalues. See problem 4.14 of Astrom and Murray for a description of the transformed coefficient matrix. The download ModelDemo.zip contains a Matlab function modal.m to compute the modal decomposition for an arbitrary coefficient matrix, and a function ModalDemo.m to illustrate the application to a randomly 3D linear system.
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