Linear matrix inequalities (LMIs) are frequently used in control engineering to design controllers and observers. Controllers and observers are dynamic systems described by differential equations that drive a technical system into a desired operating state or reconstruct certain quantities, so-called system states (possibly not measurable). To design these dynamic systems, it is necessary to solve the LMIs. This is achieved by choosing decision variables (matrices) within these LMIs such that the inequalities are satisfied. Selecting these decision variables is not trivial and significantly affects the quality of the controller and observer design. In some cases, the given structure of the decision variables (full matrix, diagonal matrix, etc.) leads to the LMIs being structurally infeasible.

This work first aims to analyze how the structure of the decision variables affects the structural feasibility of the LMIs. Subsequently, a method shall be developed and implemented that enables the optimal selection of the structure of the decision variables, so that the best possible controller or observer design is achieved.