AbstractInspired by the dynamic complementarity problem introduced by Mandelbaum, we define several matrix classes in terms of some integral conditions and discuss their connection with the existing class of strictly semicopositive matrices in linear complementarity theory. Using a time‐stepping approximation scheme, we establish the existence of an integrable solution to a class of index‐one linear complementarity systems (LCSs) involving these matrices, and that such a solution is ‘short‐time’ unique if the initial state belongs to a semiobservable cone defined in the recent paper (IEEE Trans. Autom. Control2007, in press). In contrast to the existing well‐posedness theory for the LCS, our result is based on a well‐known matrix property that has not been used in the LCS literature before. Copyright © 2007 John Wiley & Sons, Ltd.