This paper focuses on the problem of quadratic dissipative control for linear discrete-time systems. We consider the design of feedback controllers to achieve asymptotic stability and strict quadratic dissipativeness. Both the linear static state feedback and the dynamic output feedback controllers are considered. Necessary and sufficient conditions for the solutions of the quadratic dissipative control problems are obtained using the linear matrix inequality (LMI) approach. The main result of this paper unifies existing results on H-infinity and positive real control and it provides a more flexible and less conservative control design as it allows for a better trade-off between phase and gain performances.