DFT based model simplification and its applications in controls

The issues of model simplification, stabilization and control of time-delay systems are addressed. Locating unstable poles is essential in a classical stabilization problem. Since a transfer function of an infinite dimensional system is not rational, search of its poles in the entire complex plane is not a simple task. The application of DFT (discrete Fourier transform) based approximation can completely avoid such a search. This technique is discussed. It is shown that a finite dimensional controller can be obtained from the finite dimensional approximated transfer function G´(s) immediately. The technique is detailed. Procedures for evaluating unstable poles, designing controllers and computing the coprime factorizations for infinite-dimensional systems are described