On the orbital stability of periodic trajectories of a class of discontinuous systems

Abstract

This paper focuses on the stability analysis of periodic trajectories for non-autonomous systems whose right-hand sides are time-periodic discontinuous functions. Such systems arise, in particular, in optimal control problems for nonlinear control systems with periodic bang-bang inputs. We obtain sufficient orbital stability conditions of the Andronov-Witt type for this class of systems. The proposed stability conditions are applied to the analysis of periodic extremal trajectories of the controlled nonlinear chemical reaction model.