Dissipative control for linear systems via PID controller

In this paper a new type of proportional-integral-derivative (PID) controllers is designed to make the closed-loop linear system asymptotically stable and strictly quadratic dissipative. First, we give a state-space realization for such PID controller and then derive the state-space realization of closed-loop system. Second, a necessary and sufficient condition ensuring the closed-loop system to be asymptotically stable and quadratic dissipative is derived in terms of linear matrix inequality (LMI). Based on this result, the explicit expression for the PID controller gains is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design approach.