Nonnegative control of finite-dimensional linear systems

Abstract We consider the controllability problem for finite-dimensional linear autonomous control systems with nonnegative controls. Despite Kalman condition, unilateral nonnegativity constraint may cause a positive minimal time. When this happens, we prove that, if matrix of system has real eigenvalue, then there is time in space Radon measures, which consists finite sum Dirac impulses. all eigenvalues are real, unique and number impulses less than half dimension space. also focus on corresponding to finite-difference spatial discretization one-dimensional heat equation Dirichlet boundary controls, provide numerical simulations.