This paper addresses the problem of limit-cycle taming,
which is defined in this paper as the use of
nonlinear control laws to ensure that the
limit-cycle behaviour of the system beyond the
stability boundary is of a benign rather than a
destructive nature. Specifically, we consider a
one-parameter (denoted by λ) autonomous dynamic
system having algebraic nonlinearities. We assume
that the system has a stable solution, x = 0, for λ
< λ0, and experiences a Hopf
bifurcation at λ = λ0. Using a singular
perturbation analysis about the stability boundary,
it is shown that, using a simple nonlinear control
law, limit-cycle taming is always possible in the
neighbourhood of a Hopf bifurcation. The control
system proposed for limit-cycle taming is fully
nonlinear, and therefore does not affect the linear
behaviour of the system (in particular its stability
characteristics). Hence, limit-cycle taming may be
used in conjunction with a standard linear active
control (e.g. use of linear active control to
increase the stability boundary). Applications of
the theory to the problem of flutter are
presented.