The Lyapunov condition is a mathematical criterion used to assess the stability of dynamical systems. It involves finding a Lyapunov function, which is a scalar function that helps determine whether the system will return to equilibrium after a disturbance. If the function decreases over time, the system is considered stable. In control theory, the Lyapunov condition is essential for designing controllers that ensure system stability. By analyzing the behavior of the Lyapunov function, engineers can predict how systems respond to changes and optimize their performance, making it a crucial tool in fields like robotics and aerospace engineering.