Impulse free interconnection of dynamical systems

In this paper we address the problem that impulses might occur when a to-be-controlled plant is connected to a suitable controller. In the behavioral literature this issue is dealt when studying the so-called ‘regular feedback interconnection’ (RFI) of the plant and the controller behaviors. We address the question of when a given controlled behavior satisfying desired specifications can be obtained by RFI of the plant and some suitable controller. The paper presents an algorithm to construct a controller that yields the controlled behavior by RFI, if such a controller exists, and then parametrizes all such controllers. We extend the results to the more general case when all the to-be-controlled variables might not be available for interconnection. We show that any disturbances in the plant continue to remain free in the controlled behavior if and only if the interconnection is an RFI. This is also equivalent to the well-posedness of an interconnection. This paper also makes concrete the intuitive relation between absence of inadmissibility of initial conditions and RFI. A door closing mechanism is analysed in relation to the results in this paper.