State Space Representation

Learned in SE380.

State

The state $x(t)$ of a system is a collection of variables such that if we know $x(t_0)$ and the input signal $u(t)$,$t\in [t_0,t_1]$, then we can compute $x(t_1),y(t_1)$

State Space Form

The state of a system is a collection of variables which describe the evolution oft he system until the current time.

Generally, the state-space representation of a system is given by: $\{\begin{array}{l}\dot{x}(t)=f(x(t),u(t))\\ y(t)=h(x(t),u(t))\end{array}$

Warning

The dynamics of the system are defined by $\dot{x}(t)$, not just $x(t)$.

This tells us how the state changes over time.

Related

• Linearization (Control Systems)