Why do stabilizing controllers stabilize?
The paper entitled exaggerately ``Why do stabilizing controllers stabilize'' refers to the very popular behavioral approach in systems sciences. Recently, numerous trials to adopt this methodology in control appeared. The author considers feedback interconnections where all plant variables are available to the controller. Her aim is to find an appropriate controller for a given plant. The behavioral approach is employed as a general alternative way when the classical framework can not be used. The main definitions are presented and the problem is solved by using polynomial matrix theory. However, it should be noted that the paper is very hard to read. This is due to the concise argumentation without additional explanations. One example does not help very much. It seems that the paper is meant mainly for people familiar with this approach. Moreover, it seems that the main definition of systems interconnections, taken from Willems, does not cover all possibilities. For example, considering feedback interconnection from the circuit theoretic point of view, we can obtain non-stable trajectories in the positive feedback of stable circuits. Hence, we can obtain in the interconnected system new trajectories forbidden for both subsystems considered separately.
scientific article; zbMATH DE number 768878