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This article hasn't explained what a state variable is. Equally important, it hasn't explained what a state variable is not. What does it mean to be a state variable? What do temperature, pressure, and all the other variables listed have in common?

Not sure who wrote the above.... but my comment is - in the main article, there is uncertainty about the difference (if any) between a "state vector" and a "state". The article starts off with introducing the idea of a 'state variable'. And then it introduces the 'state vector'. So far so good. But then, magically it starts talking about a 'state', such as 'next state'. The question here is - what do they mean by 'state' and 'next state'? Does 'state' mean the actual quantities (actual values) of state variables at a particular time, t? Or does it mean the collection of state variables represented as a random distribution at time t? The problem here is.....they suddenly start using the word 'state' by magic. It will be good for the article to define the meaning of a 'state' clearly - with very clear examples. Like, if 'state' means the same thing as 'state vector', then it needs to be indicated. What needs to be defined properly (for example) is : the following vector [x1(t) x2(t) x3(t)], where 't' is just a time variable. Is it a state vector 'function'? And if we then write [x1(to) x2(to) x3(to)], where t = to. Then is this referred to as a "state" (at t = to)? Or is it a "state vector" at t = to? KorgBoy (talk) 15:13, 17 August 2017 (UTC)[reply]

Also, I do agree that definitions of 'state variable' tends to be vague and wishy-washy, or there are different ambiguous takes of it. To me, it seems that a state variable is a minimum set of system variables (eg. current through a component, and voltage across another component etc.) that are used within a set of equations (called state equations) that fully describe the behaviour of the system at any time - relative to an initial reference time, and for a known/given input. This can mean that the set of variables doesn't have to be unique - just as long as it is a minimum set of variables needed to mathematically describe the system behaviour (for a known/given input) at any time. What really concerns me are sources of information teaching state-space techniques, but people are confused right from the beginning due to no effort being used to properly define terms like 'state variable' and 'state'. Yes, they may have descriptions, but often over-the-top. And over-the-top is next to meaningless for people trying to understand the topic. KorgBoy (talk) 07:54, 19 July 2017 (UTC)[reply]

My Engineering Dynamics text book has an entire chapter devoted to the "State variable" approach. I was reading this article and wondering of the material I have been learning about in school would belong here. The essential concept is that newton's laws are based on a second order differential equations, and the first step in creating using the state variable approach is to convert all the differential equations into coupled first order differential equations. When this is done, the equations are written in "Standard state variable form" which I am not really seeing in this article just yet. Well I am off to class right now, but I am thinking that I have some sourced material to contribute to this article. One problem is that the word "state variable" is used in a number of different fields, and I fear that I might momentarily add to much content on the definition of state variable from a mechanical context, and I would also add that "State variables" I believe also are found in thermodynamics and quantum mechanics, and so at some point someone more well schooled in content organization will need to contribute to these efforts.

With this being said, I am off to my classes, but would like to get some feed back from others before considering adding any content here. I also would like to take some time to re-read the text I am studying and see what portions of it are suitable for an encyclopedia of this nature. So what does every body else think, back soon with some well referenced material for addition to this fine article.StressTensor (talk) 20:06, 26 April 2010 (UTC)[reply]

To continue with the plan of changes I am proposing I was considering using

System Dynamics By William J. Palm III ISBN 978-0-07-352927-1

Chapter 5 of this book is titled "State-Variable Models and Simulation Methods"StressTensor (talk) 17:09, 28 April 2010 (UTC)[reply]

Does everybody agree that the "standard form" of the state equation is that given by Palmer?. His contention for the standard form appears on page 229 of his book. I am going to attempt to render his equations slowly but my skill with writing equations in Wikipedia leaves a great deal to be desired. Anybody can help with this:

(work in progress)

${\displaystyle \mathbf {x} (dot)=\mathbf {Ax} +\mathbf {Bu} }$

${\displaystyle \mathbf {y} =\mathbf {Cx} +\mathbf {Du} }$

I would really like the dot to appear over the x indicating it is the first time derivative. —Preceding unsigned comment added by StressTensor (talk • contribs) 20:20, 5 May 2010 (UTC)[reply]

A good way to improve the "state variable" article is to include counter examples that are not state variables. Heat and work make for two. A non-state variable not affiliated with thermodynamics would really help the "state variable" article. Can anybody think of any? --guyvan52 (talk) 15:20, 2 April 2014 (UTC)[reply]

I propose to add something like this:

A variable is not a state variable if it has no bearing on the condition of a system. Examples include:

• Heat and Work (Thermodynamics)
  

Heat and work are forms of energy that can be transferred into and out of a thermodynamic system. During each cycle of a heat engine, the work done by the system exceeds the work done on the system, so that over time a net amount of energy in the form of work flows out of the system. Energy conservation is preserved by the fact that more heat flows into a heat engine than out (during each cycle). (The reverse is true if the engine is operated as a refrigeration unit).

• We really need another example here!--guyvan52 (talk) 15:37, 2 April 2014 (UTC)[reply]

Try this --guyvan52 (talk) 15:50, 2 April 2014 (UTC). And this Berry Phase article. We now have three systems with non-state variables. While Berry Phase is way beyond most reader's comprehension, the quantum phase of a wavefunction is obviously not a state variable, as anyone who knows quantum theory will assert.--guyvan52 (talk) 16:40, 2 April 2014 (UTC)[reply]

• • I'm assuming (in the context of state-space system models) that state variables are variables that belong to a set containing 1 or more variables that constitute a *minimum number* of variables needed to define (or describe) particular dynamic activity associated with that system. KorgBoy (talk) 10:52, 9 September 2017 (UTC)[reply]

The section on control engineering says

The equations relating the current state and output of a system to its most recent input and past states are called the state equations.

My understanding is that only the equations relating the current state to past states and inputs are called state equations, whereas the equations for the outputs are called the output equations. Comments? Loraof (talk) 21:40, 12 December 2016 (UTC)[reply]

• Last call for objections--if there are none, I'm going to change the wording of the article so that output equations are no longer included as state equations. Loraof (talk) 21:57, 14 December 2016 (UTC)[reply]

I included some of the above-mentioned whishes: A context of general observables of states within the setting of C*-algebras, which is the abstract mathematical background for Thermodynamics, Statistical Physics and (Quantum) Field Theory, and a section of Non-Examples including heat (with important reference) and work.

I tried to distinguish between general abstract observables, state functions, and state variables. I'm not quite happy with the "variables" here, because they seem to be just the symbol for the values of dependent or independent state functions or observables: If one has a function f: X -> Y, then one makes x an independent variable to denote elements of X and y a dependent variable to denote elements of y, with y=f(x). Here, the notion of "variables" is rather due to historic reasons and tradtion, whereas the current abstract notion is the definition of a function (as a certain subset of the Cartesian product X x Y, namely the graph of the function f as a left-total right-unique relation). But the language of "variables" has been kept in practice, although this language rather belongs to the construction of free algebras or formal languages on a set of variables.

In the C*-algebra setting, a maximal set of independent commuting observables generate a maximally Abelian sub-algebra and cann the be taken as independent variables. Formally, one could consider the free C*-algebra generated by these observables and then rightfully speak about variables in the sense of free generators, and one can express all other compatible observables as functions of the generators. This is indicated in some books, but I admit I have no direct reference so far which states it explicitely in that way; maybe, that should be related to Gleason's theorem and maybe some more explicit literature for these aspects can be found. At least, I managed to formalize a distinction between abstract observables and state functions: To express abstract observables as true "functions" on a "space", I use the Gelfand transform and express observables as functions on the Gelfand space, and I use states to perform a GNS-representation and represent the observables as linear operators on a Hilbert space. However, to my knowledge, the full construction by using the Gelfand space is directly possible only for a commuting set of observables. There seem to exist general representation theorems by using all GNS-representations of all states and all Gelfand spaces of all maximally Abelian subalgebras, but I haven't been able to formalize that completely or find the complete construction in the literature. Again, Emch and Sewell seem to indicate such constructions. I'd be glad, if someone could include additional references.

At least, the material is now written and therefore containend in the article, although its structure is far from being perfect. Several aspects could be shortenend and maybe presented in a tabular form and supported with illustrations. I've already some ideas for that and how to improve on that further, but additional contributions and ideas are warmly welcomed! EinMathematikerInAustria (talk) 07:15, 8 June 2026 (UTC)[reply]