Stability and robustness of planar switching linear systems

This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not

Re-verification of a Lip Synchronization Protocol using Robust Reachability

The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper, we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm. This lip synchronization protocol is an interesting case because timing aspects are crucial for the correctness of the protocol. Several versions of the model are considered: with an ideal video stream, with anchored jitter, and with non-anchored jitter

Stability of reset systems

We derive sufficient conditions for asymptotic stability of state reset systems in terms of a linear matrix inequality. The reset system is modeled as a hybrid automaton with one discrete state. The guard on the transition is a switching surface and the reset map is a projection onto a subspace of the state space. A discrete stability indicator is introduced: the projection gain. A modified version of the LMI provides a estimate of the projection gain

Causal ambiguity and partial orders in event structures

Event structure models often have some constraint which ensures that for each\ud system run it is clear what are the causal predecessors of an event (i.e. there is no causal ambiguity). In this contribution we study what happens if we remove\ud such constraints. We define five different partial order semantics that are intentional in the sense that they refer to syntactic aspects of the model. We also define an observational partial order semantics, that derives a partial order from just the event traces. It appears that this corresponds to the so-called early intentional semantics; the other intentional semantics cannot be observationally characterized. We study the equivalences induced by the different partial order definitions, and their interrelations