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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    $\begingroup$ 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. $\endgroup$ – copper.hat May 9 '12 at 2:51

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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  • $\begingroup$ +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. $\endgroup$ – Tim May 9 '12 at 14:53
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    $\begingroup$ Yes. And that is the time variant case I mentioned. $\endgroup$ – Shiyu May 10 '12 at 8:21

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