Analysis, Control and Synchronization of nonlinear systems and networks via Contraction Theory: theory and applications

The aim of the Thesis is that of providing a coherent theoretical framework for the study of networked systems, modeled by means of Ordinary Differential Equations(ODEs) with applications to biochemical networks. In particular, our interest is twofold. For interconnected systems, we explore the dynamical mechanisms which are responsible for the emergence of some coherent (coordinated) network dynamics. From the control viewpoint, we are interested in providing guidelines for the design of decentralized communication strategies (or protocols) for the network nodes which ensure some desired form of coordination. For biochemical systems, the analysis is focussed on understanding the key dynamical properties which are responsible for the system’s behavior, or functionality. The main results for the analysis/control of interconnected systems that are presented in the Thesis are based on the use of a generalized version of contraction theory.

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