A method for asymptotic integration of a periodic singularly perturbed system with impulses and its application in the theory of optimal control (Q1085422)

The paper deals with a singularly perturbed system of linear ordinary differential equations with constant impulses at given moments. Using the method of boundary layer functions the authors prove the existence of a periodic solution and derive an asymptotic expansion of this solution. The approach is applied to a problem for periodic optimal control of a linear singularly perturbed system with a criterion depending on the state value at given moments of time where the adjoint system contains impulses.