Lyapunov's second theorem

Lyapunov’s second theorem provides a way to determine whether a system will remain stable over time. It involves finding a special function, called a Lyapunov function, that acts like an energy measure. If this function always decreases or stays constant as the system evolves, then the system is stable—it won't diverge or behave unpredictably. Think of it as a mathematical tool that confirms if a system naturally tends to return to equilibrium after disturbances. This theorem is fundamental in control theory for designing and analyzing stable dynamic systems.