In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system.
In 2004, Massera's original lemma for single variable functions was extended to the multivariable case, and the resulting lemma was used to prove the stability of switched dynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals.
Massera’s lemma is used in the construction of a converse Lyapunov function of the following form (also known as the integral construction) for an asymptotically stable dynamical system whose stable trajectory starting from
be a positive, continuous, strictly decreasing function with
be a positive, continuous, nondecreasing function.
such that Massera's lemma for single variable functions was extended to the multivariable case by Vu and Liberzon.
be a positive, continuous, strictly decreasing function with
be a positive, continuous, nondecreasing function.