# Thread: State-space Model of a dynamic system - Nomenclature problem

1. Do we define 'State-space model' of a dynamic system:

, generic implicit representation of a vector-state system,

or:

, implicit representation of a linear vector-state system?

ps: state vector, time variable, vector of inputs, matrix of dynamics, ...

2.

3. Originally Posted by doctor_cat
Do we define 'State-space model' of a dynamic system:

, generic implicit representation of a vector-state system,

or:

, implicit representation of a linear vector-state system?

ps: state vector, time variable, vector of inputs, matrix of dynamics, ...

You can do it either way.

Your first definition is very general.

The second definition is the linear case. In the linear case there is enough restriction on the form of the dynamical system to allow the use of additional mathematics to study such systems in detail. This sort of thing is covered in electrical engineering books on "linear systems" and "linear control theory". See for instance Brocket's Finite Dimensional Linear Systems[i/]

The non-linear case is also studied, but only with some additional constraints on the form of the forcing function f, With no constrainst on f at all literally anything can happen. There are sll sorts of books on non-linear dynamical systems, and what you might want to look at depends greatly on taste.

4. I thank you!

My question is only about nomenclature unfortunately:

there are several books to study the behavior of dynamics systems but I can't find which representation 'State-space Model' refers to.

5. Originally Posted by doctor_cat
I thank you!

My question is only about nomenclature unfortunately:

there are several books to study the behavior of dynamics systems but I can't find which representation 'State-space Model' refers to.
1. Most books on state-space analysis use the linear model. But on the other hand most books are about the linear theory.

2. If your book is not clear on what the term means as used in the book, I would get a better book.

3. What is the title of your particular book ?

6. I use 4 specific books (about Theory of systems - e.g. Luenberger - Introduction to dynamic systems).

I need the meaning of the term "State-space model" as used everywhere (even in MatLab software, if you submit 'help ss', you can read the term), not only in my books.

7. Originally Posted by doctor_cat
I use 4 specific books (about Theory of systems - e.g. Luenberger - Introduction to dynamic systems).

I need the meaning of the term "State-space model" as used everywhere (even in MatLab software, if you submit 'help ss', you can read the term), not only in my books.
Luenberger treats both linear and non-linear systems. When you are talking about linear systems the linear formulation applies. When you are talking about general dynamical systems the more general formulation applies.

In the table of contents for the book I notice that the term "state space methods" occurs in a section that indicate an emphasis on the linear models common to control theory.

Note that the linear formulation is a special case of the general formulation so there is never a conflict.

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