In this paper cone-copositive piecewise quadratic Lyapunov functions (PWQ-LFs) for the stability analysis of conewise linear systems with the possible presence of sliding modes are proposed. The existence of a PWQ-LF is formulated as the feasibility of a cone-copositive programming problem which is represented in terms of linear matrix inequalities with equality constraints. An algorithm for the construction of a PWQ-LF is provided. Examples show the effectiveness of the approach in the presence of stable and unstable sliding modes.