  The impulsive Goodwin's oscillator (IGO) is a hybrid model composed of a
third-order continuous linear part and a pulse-modulated feedback. This paper
introduces a design problem of the IGO to admit a desired periodic solution.
The dynamics of the continuous states represent the plant to be controlled,
whereas the parameters of the impulsive feedback constitute design degrees of
freedom. The design objective is to select the free parameters so that the IGO
exhibits a stable 1-cycle with desired characteristics. The impulse-to-impulse
map of the oscillator is demonstrated to always possess a positive fixed point
that corresponds to the desired periodic solution; the closed-form expressions
to evaluate this fixed point are provided. Necessary and sufficient conditions
for orbital stability of the 1-cycle are presented in terms of the oscillator
parameters and exhibit similarity to the problem of static output control. An
IGO design procedure is proposed and validated by simulation. The nonlinear
dynamics of the designed IGO are reviewed by means of bifurcation analysis.
Applications of the design procedure to dosing problems in chemical industry
and biomedicine are envisioned.
