Matrosov Theorem

Matrosov’s Theorem is a tool in control theory used to prove the stability of complex systems, especially when traditional methods fail. It extends Lyapunov’s direct method by using multiple auxiliary functions, called Matrosov functions. If these functions collectively demonstrate that the system's energy or deviation from a desired state decreases over time, the system is considered stable. Essentially, it provides a systematic way to confirm stability in systems where a single simple test isn't sufficient, by examining a combination of conditions that together ensure the system's behavior remains controlled and predictable.