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Robust quadratic dissipative control for a class of linear multi-variable systems with pa- rameter uncertainties is considered,where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties,the equivalence between quadratic dissipativeness and positive realness is established,and conditions are derived for linear systems to be quadratic dissi- pative.As for uncertain systems,it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties.The control problem concerned can be solved using LMI approach.The results of the paper unify existing results on H_∞control and positive real control and provide a more flexible and less conservative control design method.
For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissi- pative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties.The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H_∞control and positive real control and provide a more flexible and less conservative control design method.