What is a Control System?
May 12, 2023
A control system is a dynamical system that should be led to a desired dynamical behavior and performance with the aid of a control input. The dynamical system to be controlled is modeled mathematically by a set of differential equations,
$$ \begin{align} \dot{x}(t) &= f(x(t),u(t),t)\\ y(t) &= g(x(t),u(t),t) \end{align} $$Where $x(t)$ is the state of the system. The state describes the dynamical behavior of the system from an initial condition until a desired state.
The $u(t)$ is the input or admissible controls of the system. The output of the system is $y(t)$. Typically, the output signal depends on the system state.