Difference time-variant/invariant vs dynamic/static What is the difference of the property of the system being time-variant or time-invariant and the property being dynamic or static? In [1] a dynamic system was defined as system where the output depends not only on the current input but the history of inputs, so it is time variant. So these two properties seemingly mean the same. But reading other literature I am not sure, because they sometimes speak about "Time-Invariant Dynamic Systems" for example. I am confused, how can a system be time-invariant and in the same time dynamic?
[1] NELLES, Oliver: Nonlinear system identification: from classical approaches to neural net- works and fuzzy models. Springer Science & Business Media, 2001
 A: Lets say that I have a system: I drive my car down a straight road. The input to the system is how much I press the gas pedal (all other inputs such as steering etc. are assumed to be zero) and the output of the system is how far the car has traveled in meters. This system is dynamic: how far the car has traveled depends on how the gas pedal has been moved historically, not just on how I press it right now.
For most cars, this system would be time-invariant. It doesn't mater if I start driving at 11AM or 2PM or today or next year, the car will respond in the same way to gas pedal presses. The system is not directly dependent on time. 
If the software on my car made it accelerate slower between 10PM and 2AM (maybe this is something the manufacturer has added to improve safety at night), my car would be time-variant. Now the behavior of the car is directly dependent on time.
The first example would be a time-invariant dynamic system. The second example would be a time-variant dynamic system. 
A: A dynamic system is exactly what u said. The output depends on current and past input values. If a dynamic system is time invariant then the relationship between input/output does not change in time. For example, you have an impulse response and u just convolve it with the input to calculate the output.  A time varying system on the other hand, changes through time. So when u are using a model to approximate it then the model coefficients are gonna evolve through time. Back to the example with the impulse response, now in order to get the output you have to convolve ur input with an impulse response that changes for example its shape through time. The output still depends on past input values but now the relationship between input/output is not fixed anymore.
