Abstract. Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Reference [9] proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers. This paper aims at generalizing the idea, relying on existing methods from Control Theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems. While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants.

This paper addresses the Internet of Things (IoT) paradigm, which is gaining substantial ground in modern wireless telecommunications. The IoT describes a vision where heterogeneous objects like computers, sensors, Radio-Frequency IDentification (RFID) tags or mobile phones are able to communicate and cooperate efficiently to achieve common goals thanks to a common IP addressing scheme. This paper focuses on the reliability of emergency applications under IoT technology. These applications' success is contingent upon the delivery of high-priority events from many scattered objects to one or more objects without packet loss. Thus, the network has to be selfadaptive and resilient to errors by providing efficient mechanisms for information distribution especially in the multi-hop scenario. As future perspective, we propose a lightweight and energyefficient joint mechanism, called AJIA (Adaptive Joint protocol based on Implicit ACK), for packet loss recovery and route quality evaluation in the IoT. In this protocol, we use the overhearing feature, characterizing the wireless channels, as an implicit ACK mechanism. In addition, the protocol allows for an adaptive selection of the routing path based on the link quality.

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