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.<>