Decide on terminology: equilibrium point vs operating point

[Richard Murray]

On 1 Oct 2015, Andre Tits said:

Another thing (which you may or may not like) which I do differently from your book, a matter of terminology this time. In Section 6.1, for xdot=f(x,u), you talk about "equilibrium point" (xe,ue). I use the term "operating point" instead. (Indeed, roughly speaking, for every ue, there exists an xe such that (xe,ue) satisfies the conditions, so that set of such points is uncountable, which to me does not fit well with "equilibrium point".) Again, just a thought.

On 4 Oct 2017, Karl said:

It is very clear what we mean by equilibrium for an autonomous system xdot = f(x).

I fully agree with Andre' that it is less clear when xdot = f(x,u) and I like the ideal to use the word operating point. It also fits well into linearization when we are exploring behaviors around a particular operating point. My immediate reaction is that we should introduce operating point at appropriate places. A related question is if we should use the notation xe ue or if we should use another notation.

[Richard Murray]

Discussion with Karl on 24 Jul:

• Equilibrium point = mathematical definition of special point for dynamical system.
• Operating point = place that you would like to operate the system.

Don’t want to change the x_e, u_e notation at this stage.

[Richard Murray]

Went through and checked/cleaned up the language. Also changed “equilibrium” to “equilibrium point” and “equilibria” to “equilibrium points”. See https://bitbucket.org/murrayrm/fbsbook/wiki/Terminology.

[Richard Murray]

Resolved in commit 6f3f4a5.