Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems

This paper deals with the well-posedness of a class of complementarity dynamical systems. Both the linear and the nonlinear cases are treated, and the systems are non-autonomous. A specific "input-output" property is used to perform a change of state vector which allows one to transform the complementarity dynamics into a perturbed Moreau's sweeping process. Then the results obtained by J. F. Edmond and L. Thibault ["Relaxation of an optimal control problem involving a perturbed sweeping process", Mathematical Programming 104 (2005) 347--373; and "BV solutions of nonconvex sweeping process differential inclusions with perturbation", Journal of Differential Equations 226 (2006) 135--179] and L. Thibault ["Sweeping process with regular and nonregular sets", Journal of Differential Equations, 193 (2003) 1--26] on the well-posedness of the sweeping process are used. Absolutely continuous as well as bounded variation solutions (with state jumps) are examined in this work.