Dynamical Systems

Descibes the change in the state of a system over time. More formally, it describes the evolution of the state of a system.

Linear Time-Invariant System

Many systems behave in a way described by Linear Time-Invariant (LTI) systems. It consists of a control input that is going to force a change in the state of the system, and a measured output that represents the current state of the system. The control input is sometimes called a forcing input. We presume that we would have some control over the system and that the control input would be able to change its state over time. A system that changes over time is called a dynamical system.

A Linear Time-Invariant system, as the name suggests, has two parts to it:

Linear - If we apply an input a and then an input b, it's the same as applying the input b and then the input a.

• If we apply an input a and get a response r, applying an input 2Xa will give the response 2Xr.

Time Invariant - This means that applying an input right now has the same effect as applying an input 5 seconds from now.

Non-Linear Systems

References

• FRC Documentation Simulation Physics