State-Space GlossaryΒΆ


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 inputs to drive a system to a desired state, given the current state. A common example is the control law \(\mathbf{u} = \mathbf{K(r - x)}\)


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


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

system identification

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


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


\(\hat{\mathbf{x}}\), or x-hat: the estimated state of a system, as estimated by an observer.