ABSTRACT
A major problem to be faced when designing a feedback policy is that the resulting feedback configuration may be unstable, even though both the economy and the policy rules may themselves be stable. What we mean by 'unstable' is that even a short, isolated exogenous disturbance, or change in the level of the desired reference variable, will provoke a catastrophic, ever-increasing deviation of the economy from the desired time path. In mathematical terms, this will happen if the characteristic polynomial of the set of difference equations, which describe the behaviour of the economy under feedback control, has any roots that have magnitude greater than unity. (We maintain the assumption, made in the previous chapter, that the economy is described by a linear model.)
The designer has to work with 'open-loop' entities, namely the model of the economy without feedback, and the policy he is designing. The problem of deducing whether the 'closed.loop' system will be stable, from the open-loop information available to him, is solved by the Nyquist stability theorem, which will be presented in the next section. This theorem leads to a design technique that allows one to specify the transfer function of the economic policy in such a way as to obtain satisfactory closed-loop regulation properties, with the assurance that closed-loop stability is not lost.
