Structural vibration mitigation using semiactive control strategies has received special attention recently due to the attractive properties of semiactive devices. The main restriction of a semiactive device is that it can only produce dissipative forces, which may be expressed in mathematical terms as a nonlinear inequality constraint. Standard active control algorithms do not generally account for this kind of constraint. In this paper, the nonlinear dissipativity constraint is integrated into the well-known linear quadratic regulator (LQR) algorithm using linear matrix inequality (LMI) techniques to be utilized in the semiactive control of the structures. First, the linear quadratic regulator problem is recast as an eigenvalue problem (EVP) in terms of LMIs. Then, the dissipativity constraint is appended in weak expected value form to the other constraints in the EVP. The proposed method is demonstrated in semiactive control of a 2-DOF structural system. It is found that although the dissipativity constraint is represented in its weak form, the proposed method yielded control forces more dissipative than standard H/sub 2//LQR methodologies.