On The Lyapunov Theory: Application To LTI Systems
This brief paper is a review of the classical Lyapunov theory, also referred to as Lyapunov’s direct method or Lyapunov’s second method. The Lyapunov theory uses the concept of Lyapunov function of the system to draw conclusions on system stability, without actually solving the differential equation of the system motion. Some primary definitions are recalled and uniqueness solution issue for the Lyapunov equation is addressed for linear systems.
Key words: Asymptotic Stability, Lyapunov Stability, Lyapunov function, Linear Time Invariant System (LTI).
