Investigation of dissipativity for control of smart dampers via LMI synthesis

This paper investigates the effects of dissipativity on the performance of semiactive systems with smart dampers via linear matrix inequality (LMI) methods. First, a linear quadratic regulator (LQR) problem is defined in terms of a linear objective function and several LMI constraints. Second, two dissipativity indices are proposed to quantify the dissipative nature of a force. One of the dissipativity indices is appended as an LMI constraint in its weak form to the LMI-LQR problem to exploit the dissipative nature of a smart damper. The dissipativity indices and the proposed controller are employed for a two-degree-of-freedom structure with a clipped optimal control problem. It is observed that the proposed method is able to improve the dissipative nature of the controller, improving the semiactive performance.