Dissipative control of linear discrete-time systems with dissipative uncertainty

This paper focuses on the dissipative control of uncertain linear discrete- time systems. The uncertainty under consideration is characterized by a dis sipative system,which contains commonly used uncertainty structures, such a s norm-bounded and positive real uncertainties, as special cases. We consid er the design of a feedback controller which can achieve asymptotic stabili ty and strict quadratic dissipativeness for all admissible uncertainties. B oth the linear static state feedback and the dynamic output feedback contro llers are considered. It is shown that the robust dissipative control probl em can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. Linear matrix inequality (LMI) based methods for desi gning robust controllers are derived. The result of this paper unifies exis ting results on discrete-time H-infinity and positive real control and it p rovides a more flexible and less conservative control design as it allows f or a better trade-off between phase and gain performances.