Synthesis of a closed loop transfer function with aid of finite Hilbert transforms

The objective of satisfying assigned performance tolerances over given ranges of plant uncertainty and external disturbances is achieved by synthesis of the closed-loop transmission function L(ω) along frequency dependent, boundaries ψ(ωn) within the Nichols chart. The corresponding frequency bandlimited equations are recognized as those of Carleman. Their solutions are given by closed form expressions involving finite Hilbert integrals. Some numerical examples of such solutions are then presented.