Abstract:

When we do not know the matrices defining the system and it has no zeros, but the output power spectrum is known, we use the spectral factortzation to resolve the spectral factor of the system and we can recover the system through this method. Descriptor systems are changed into normal subsystems by using Jordan decomposition of matrices while keeping the observability. We can solve a zero free minimum phase spectral factor of the normal linear subsystem, and from this spectral factor we can have a zero free minimum phase spectral factor. At last, a numerical example is given to illustrate the methods.

Key words: discrete-time descriptor systems, spectral factorization, Riccati equation, spectral factor