From Bill Silvert (931222.0824 AST)

From Bob Clark (931221.1615 EST)

STABILITY

I believe that "stability" is a necessary, but not sufficient,

condition for control. That is, control (good control, I mean)

produces stability, but stability can result from other processes as

well.

I think of "stability" as a "characteristic" of some combinations of

components. Some negative feedback control systems do operate to

"stabilize" some variables. But the control systems considered in

PCT are "closed through the environment," hence their stability is

contingent on the characteristics of the environment. The complete

combination is not _necessarily_ stable.

My dynamics book defines stable, unstable and "aymptotically" [I think

you mean "symptotically"] stable in the context of systems

without input.

This dialogue reflects the dynamical systems theory mindset, but

feedback systems can be regulated in an unstable way. For example, a

thermostat switches a furnace on and off. In either state the system is

far from stability (the stable temperature is perhaps 40 C when the

furnace is on and -10 C when it is off), but the temperature oscillates

around 20 C. So one can have control without stability.

Reference:

Silvert, William. 1983. Is dynamical systems theory the best way to

understand ecosystem stability? In "Population Biology",

H. I. Freedman and C. Strobeck, eds.

Springer-Verlag Lecture Notes in Mathematics 52, pp. 366-371.

This dialogue reflects the dynamical systems theory mindset,

I must be guilty of Impure Thoughts. The forces of Satan are always at

work. ;->

but

feedback systems can be regulated in an unstable way. For example, a

thermostat switches a furnace on and off. In either state the system is

far from stability (the stable temperature is perhaps 40 C when the

furnace is on and -10 C when it is off), but the temperature oscillates

around 20 C. So one can have control without stability.

Actually, this is an example of stability. If the temperature

oscillates in a region, say 20 C +/- 40 C, then this would fit the

description of "stability" but not "aymptotic stability". This is a

limit cycle attractor, not a point attractor. Just because the

accuracy is low makes no qualitative argument about stability.

O----------------------------------------------------------------------------->

Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA

Systems Science, SUNY Binghamton NASA Goddard Space Flight Center

cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .

This may fit the `description of stability' but not the definition.

Of course if one defines scientific concepts intuitively, and everyone

uses his/her own definition, then we are all right and there is no basis

for disagreement. The key to a perfect world?

Bill Silvert [93-12-28, 17:00 AST]

## ยทยทยท

feedback systems can be regulated in an unstable way. For example, a

thermostat switches a furnace on and off. In either state the system is

far from stability (the stable temperature is perhaps 40 C when the

furnace is on and -10 C when it is off), but the temperature oscillates

around 20 C. So one can have control without stability.

Actually, this is an example of stability. If the temperature

oscillates in a region, say 20 C +/- 40 C, then this would fit the

description of "stability" but not "aymptotic stability". This is a

limit cycle attractor, not a point attractor. Just because the

accuracy is low makes no qualitative argument about stability.