# State-Space Glossary¶

dynamics

A branch of physics concerned with the motion of bodies under the action of forces. In modern control, systems evolve according to their dynamics.

control law

A mathematical formula that generates to drive a to a desired , given the current . A common example is the control law $$\mathbf{u} = \mathbf{K(r - x)}$$

gain

A proportional value that relates the magnitude of an input signal to the magnitude of an output signal. In the signal-dimensional case, gain can be thought of as the proportional term of a PID controller. A gain greater than one would amplify an input signal, while a gain less than one would dampen an input signal. A negative gain would negate the input signal.

hidden state

A that cannot be directly measured, but whose can be related to other states.

measurement

Measurements are that are measured from a , or physical system, using sensors.

system identification

The process of capturing a in a mathematical model using measured data. The characterization toolsuite uses system identification to find kS, kV and kA terms.

x-dot

$$\dot{\mathbf{x}}$$, or x-dot: the derivative of the vector $$\mathbf{x}$$. If the had just a velocity , then $$\dot{\mathbf{x}}$$ would represent the 's acceleration.

x-hat

$$\hat{\mathbf{x}}$$, or x-hat: the estimated of a system, as estimated by an .