Description of switched systems by implicit representations

This paper shows that a certain class of time-dependent, autonomous switched systems can also be studied using the structural concepts and properties of the linear time-invariant implicit systems theory. We first consider the modeling aspects, and then, the control aspects are tackled. This fact contributes to the enrichment of the switched systems theory and enlarges its action field. In Section I we specify a class of time-dependent, autonomous switched systems which enables us to describe systems with a variable internal structure. In Section II we show how to translate the considered class of time-dependent, autonomous switched systems into an implicit representation and then we recall some important results, of the implicit systems theory, which enable us to control them in such a way that they behave as a specified linear time-invariant system whatever be the position of the switches. In Section IV, we consider some reachability aspects. In Section V, we conclude.