Controlling systems via set-theoretic methods: some perspectives

Set-theoretic methods for analysis and design of control systems have a long history since the first contributions trace back the early 70s. The theory was almost abandoned once it became clear that, although the techniques are appropriate to solve many theoretical and practical problems, the complexity of the required algorithms was not compatible with the computer technology of the time. In recent years, the theory is receiving a renewed interest due the current computer performances which are suitable to face non-trivial problems. In this tutorial, after a due tribute to the pioneering past work, we consider the area in a new perspective. We investigate several problems that can (at least potentially) have a benefit from these techniques. The paper sketches some ideas that, although already presented in the literature, have still to be fully developed. Concepts are not presented in a formal way but explained by means of simple illustrative examples