Proprietà strutturali e garanzie di privacy di sistemi di controllo su canali di comunicazione di Markov

The aim of this thesis is presenting the structural properties and privacy guarantees of control systems connected via wireless communication channels, that are modeled through the finite-state Markov channel abstraction. Spatially distributed systems connected via wireless medium, also known as wireless control networks, are here investigated. The aforementioned structural properties are properly exploited to develop a stability analysis specific for wireless control network scenarios. As explained in the following chapters, there is a wide literature focusing on stability analysis, structural properties, and privacy guarantees of wireless control networks. Most of these works adopt Bernoulli random variables to model packet loss occurrences over wireless channels. However, this strategy does not allow to model the occurrence of bursts of packet losses, as Markov chain theory does. The improvement with respect to the previous works is modeling the wireless channel as finite-state Markov channel, that allows for modeling the occurrence of bursts of packet losses, as well as the current mode of the channel. As a consequence of the Markovian characterization of the wireless channel, Markov jump system theory provides good mathematical approximations of wireless control network scenarios. The contribution achieved by the research presented in this thesis is threefold. Firstly, this work investigates wireless control network scenarios with double sided packet-loss links modeled via finite-state Markov channels. Under the assumption of a TCP-like communication scheme and the mathematical framework of Markov jump linear systems, the separation principle holds also in this case with finite-state Markov channels. Secondly, the research here reported provides conditions guaranteeing secrecy against eavesdropping over finite-state Markov wireless links. Finally, the case of nonlinear discrete-time Markov jump systems is investigated with the aim of the generalization of Markov jump linear system framework, so that nonlinear plants may be involved in wireless control network analysis. Proper stability notions and Lyapunov conditions are presented for nonlinear discrete-time Markov jump systems in the case without any delay, as well as in the case of nonlinear discrete-time systems with Markovian delays. Keywords: Markov Jump Systems, Lyapunov theorems, Wireless control networks, Finite-state Markov channels