Controllability of linear and nonlinear systems governed by Stieltjes differential equations

Abstract

In this manuscript, controllability of vector valued g-derivative Stieltjes differential system is considered. For linear system, explicit solution of homogeneous case is obtained by constructing a generalized matrix exponential function and nonhomogeneous solution is achieved with transferring the corresponding problem into a class of Stieltjes impulsive differential equations. Based on the analysis techniques of linear system theory, the Gramian criterion and the rank criterion for linear case are established, respectively. Existence of local and global solution for nonlinear system are presented by the well-knonw Banach contraction principle and the controllability result for nonlinear systems is shown by Krasnoselskii’s fixed point theorem. Simulations for linear and nonlinear systems are tackled respectively to verify the efficiency of theoretical results.