An optimal stopping problem arising in almost-dissipative systems

This paper presents an optimal stopping time interpretation of an optimization problem that arises in the worst case analysis of systems which "almost" satisfy a dissipation property (such as systems with practical L₂-gain or practical integral-input-to-integral-state stability). Using this interpretation, links between the value function for the associated optimization problem and the corresponding optimal stopping time are explored, yielding conditions for finiteness, uniqueness and an explicit formula for the optimal stopping time. Furthermore, the target set corresponding to the stopped trajectory is investigated. Two simple examples are presented.