Algebraic approach to synthesis of data-driven control design for dissipativity

Model-based control methods play an important role in control theory. Such controllers are designed via system identification; however, this approach is not applicable to cases where it is difficult to execute system identification owing to the large amount of data or experimental construction. To address these problems, data-driven control methods, in which controllers are designed by directly using target input–output data, have attracted attention for their effectiveness. Thus a framework has been proposed to reevaluate the aforementioned approaches and consider them in terms of data informativity. Herein, we use this framework to address the design problem of data-driven control for dissipativity. Using an algebraic approach, we derive necessary and sufficient conditions that data must satisfy to render a system dissipative via feedback control.