Finite-Time Stability via Non Quadratic Lyapunov Functions of Nonlinear Quadratic Systems

We aim to study the synthesis of new conditions satisfying finite-time stability (FTS) of quadratic systems. An adequate choice of the form of the Lyapunov function makes it possible to group the conditions for quadratic and non quadrtic Lyapunov functions into a single theorem. The design conditions are expressed in term of linear matrix inequalities (LMIs) by combining the notion of annihilator with a version of Finsler's lemma.