  In the present work, we formulate a generalization of the Noether Theorem for
action-dependent Lagrangian functions. The Noether's theorem is one of the most
important theorems for physics. It is well known that all conservation laws,
\textrm{e.g.}, conservation of energy and momentum, are directly related to the
invariance of the action under a family of transformations. However, the
classical Noether theorem cannot be applied to study non-conservative systems
because it is not possible to formulate physically meaningful Lagrangian
functions for this kind of systems in the classical calculus of variation. On
the other hand, recently it was shown that an Action Principle with
action-dependent Lagrangian functions provides physically meaningful Lagrangian
functions for a huge variety of non-conservative systems (classical and
quantum). Consequently, the generalized Noether Theorem we present enable us to
investigate conservation laws of non-conservative systems. In order to
illustrate the potential of application, we consider three examples of
dissipative systems and we analyze the conservation laws related to spacetime
transformations and internal symmetries.
