A Stable Money Supply

Positive feedback tends to cause system instability, divergence from equilibrium, oscillation and often exponential growth. (Wikipedia).
Modern monetary systems are unstable. To address the problem any positive feedback components should be examined and if possible eliminated or alternatives made available.

In monetary systems two widely used accounting rules create positive feedback. The first is the payment of interest on interest and the second is the creation of interest bearing loans backed by money.  Both of these are accounting conventions and both can be less widely used if instability becomes an issue for any community.

Any widespread inflation of goods, services or assets is a sign of instability.  There is no safe level of inflation.

One of reasons for inflation is debt paying interest on interest that swamps interest on money backed by tangible assets. There is little justification for having interest bearing money in the system that swamps interest paid on tangible assets.

Interest on Interest

When interest is paid on interest the equation is I = I + f(I).  This is a positive feedback term and to remove it we can to set up loans so that interest accumulates but there is no interest paid on interest.  This can be achieved by ensuring that when loans are repaid the capital amount reduces, interest accumulates but there is no interest paid on accumulated interest.

Creation of Loans backed by Money

When a loan is made money is created.  Normally loans are only created if they are backed by assets.  If a loan is made and it is backed by money then the equation is M = M + f(M). This is positive feedback.  In an expanding economy it is necessary to increase the money supply through loans and so creating money backed by money is not necessarily a problem.  However there are social implications as it means that the increase in the money supply is given to the people who already have money.

An alternative is to create loans without interest and to ensure the loans are used to create new assets to back the new money.  The most obvious way to do this is with loans of benefit to a broad area of the community, as in student loans, or with infrastructure that everyone can use, such as water supply or energy supply. A good way to give the loans is to the citizens who pay for water and pay for energy.