This paper focuses on the dissipative control of uncertain linear discrete-time systems. The uncertainty under consideration is characterized by a dissipative system, which contains commonly used uncertainty structures, such as norm-bounded and positive real uncertainties, as special cases. We consider the design of a feedback controller which can achieve asymptotic stability and strict quadratic dissipativeness for all admissible uncertainties. Both the linear static state feedback and the dynamic output feedback controllers are considered. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. Linear matrix inequality (LMI) based methods for designing robust controllers are derived. The result of this paper unifies existing results on discrete-time H{sub}∞ 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.
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