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We study the construction of the maximal controlled invariant set of switched linear systems. We consider two cases, based on whether fast switches are allowed or not. For both cases, iterative algorithms are given to construct such sets.
— Given a hybrid automaton and a desired precision, we aim at constructing an approximate abstraction by means of a timed automaton, whose discrete state trajectories approximate the discrete state trajectories of the original system, with the desired precision on switching times. We show that using the Euclidian metric on reals it is not always possible to… (More)
We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the… (More)
A fundamental question in systems and control theory concerns the characterization of the set of achievable closed-loop systems for a given plant system and a controller system to be designed. This problem, for example, shows up in assessing the 'limits of performance' of a controlled system. Similar problems have been studied by researchers in automata… (More)
In this paper we discuss the concept of compatible behavior in-terconnections. We distinguish the case where all variables are available for interconnection (total interconnection) from the case where only a part of them are (partial interconnection). The main idea behind the notion of compatibility for total in-terconnection is causality of (the effect of)… (More)
In this paper we formulate a general framework based on the behavioral approach to dynamical systems, in which various issues regarding interconnection of systems can be addressed. The main part of the framework is that interconnections or compositions of systems can be modelled with interconnection of behaviors and generalized projection operations.… (More)
In this paper we present a structure called hybrid behavioral automata (HBA) as a tool to model hybrid systems. One distinct feature of HBA is the classification of the transitions into active and passive ones. With such a classification, it is possible to model unidirectional discrete synchronizations between HBA. Interconnection operations for HBA, total… (More)
— Model checking can be used to verify temporal properties of hybrid automata. However, model checking is not decidable in general. We overcome this difficulty by considering a durational graph abstraction, for which model checking is decidable. The contribution of this paper is to show that, given a hybrid automaton and the durational graph abstraction,… (More)
— We cast the notion of bisimulation in the Willems' behavioral setting. We show that in this setting, bisimulation is also a congruence, as it is known in the field of concurrent processes. Bisimulation is a congruence means if A and A are bisimilar systems, then A B and A B are also bisimilar. Here, the operator denotes systems composition, and B is any… (More)