This work deals with finite time observability of switched linear systems (SLS) when they are represented by a family of nonautonomous linear systems (LS) and an interpreted Petri net (IPN). Based on this SLS representation, new detection of the commutation time and LS distinguishability characterizations in SLS extended to the non autonomous case are presented. Using these results, the novel concept of distinguishability between LS sequences is presented and characterized. This concept together with the IPN input-output information is used to determine the IPN marking sequence. From the knowledge of this sequence, the conditions for the computation of the continuous state are presented. Also necessary and sufficient conditions for the observability in infinitesimal time are provided.

This paper deals with supervisory control of Discrete Event Systems (DES) modeled by Interpreted Petri Nets (IPN). In the approach herein proposed, both, the specification and the system model are described by IPN, however, the specification describes a state subset that the specification must reach. It also captures the order in which these states must be reached. Based on this framework, this paper presents a method to compute the system firing transition sequence in order to confine the system model into the specification behavior. Although this problem is NP-complete, the proposed solution exploits the structural information of both IPN (system and specification) to compute Parikh vectors of system firing sequences; one vector per each transition of the specification. These Parikh vectors are processed in order to obtain controllable fireable transition sequences. Thus a divide and conquer technique is used, where the NP-complete problem divided into k small size problems (where k is the number of specification transitions), reducing the computational time of proposed algorithms. Moreover, the technique herein presented is suitable for distributed and hierarchical control. All algorithms herein purposed have being implemented in MAPLE.