Frequency domain techniques in systems theory have their origins in
Heavyside's operational calculus (Heavyside, 1889). Such work was later
developed by Foster and Campbell (1931), Brune (1931), Nyquist (1932),
Black (1934), Darlington (1939) and subsequently Bode (1948). This
interest in the frequency domain was due to its appeal to the intuition of
The dominance of frequency domain techniques was subsequently eroded from
the late 1950s through the 1960s by the influence of the space programmes.
The space systems being analysed were based on strong theoretical
foundations with well-defined sets of differential equations. The analysis
led to the development of the state-space methods which were able to cope
with the multivariable problems and were amenable to numerical solution.
As a result of these developments, control engineering was largely
dominated by the state-space approach and the associated areas of LQG
optimal control, Kaiman-Bucy filters, observability and controllability.
Two factors led to a resurgence of interest amongst academics in the
development of frequency domain techniques in the 1970s and 1980s. The
first was the development of the Fast Fourier Transform (FFT) (Cooley &
Tookey, 1965). This provided an efficient method of analysing the Fourier
transforms of signals and allowed the development of spectral methods of
obtaining frequency response estimates. The collection of data was greatly
speeded up and this enabled frequency domain methods to be increasingly
applied to on-line control problems. The second factor was that the
developments in the time domain were never fully embraced by practicing
engineers in traditional control environments.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.