# Difference between state and parameters of a system

1. In my previous question, based on the information I have so far, my understanding about a system is that a system transforms an input function to an output function.

So I think all the things involved in the transformation, except input and output, are the parameters of the system. Am I right?

2. But there is another concept, the state of the system, which is neither input nor output. So I wonder if the state of the system is also part of the parameters of the system?

If yes, what distinguishes state parameters and non-state parameters of the system?

Thanks and regards!

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The term parameter is used loosely. The state typically encapsulates all past history. In my experience, the term parameter is typically used to describe something like a design or environmental parameter which remains fixed, or is 'slowly varying'. But there is no law dictating what is or is not called a parameter. –  copper.hat May 9 '12 at 2:51

## 1 Answer

If you are dealing with control systems, state is the behavior of the system you are going to control. The parameters usually are fixed and reflected in the A, B, C, D matrices (for linear systems). In certain cases, the parameters may change overtime, then A, B, C, D also change and the system is time variant.

For example, consider a robot manipulator. The mass and length of each link are the parameters. The position and velocity of the end-effector are the states. You are going to control the position and velocity (state) of the robot instead of the mass or length (parameter).

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+1 Thanks! But I think the non-state parameters can also change over time, see the state space model for Kalman filter $\textbf{x}_{k} = \textbf{F}_{k} \textbf{x}_{k-1} + \textbf{B}_{k} \textbf{u}_{k} + \textbf{w}_{k}$, where $x_k$ is state at time k, and $F_k, B_k$ are all non-state parameters and also change over time k. –  Tim May 9 '12 at 14:53
Yes. And that is the time variant case I mentioned. –  Shiyu May 10 '12 at 8:21