DATA-DRIVEN DISSIPATIVITY ANALYSIS

Abstract

This thesis focuses on the formulation of data-driven dissipativity conditions within a behavioral framework for discrete LTI systems. Traditional approaches to dissipativity require explicit system models and often rely on assumptions such as system controllability and input-output partitioning of the variables. This research aims to circumvent these limitations by utilizing a recently developed result for system identification that do not rely on these assumptions. The study presents a novel methodology that leverages the generalized fundamental lemma, allowing for the identifiability of LTI systems from trajectory data without the need for persistently exciting inputs or prior knowledge of system controllability, thus overcoming the conservativeness imposed by persistency of excitation condition, popularly known as Willems’ fundamental lemma . This method significantly broadens the applicability of dissipativity analysis, making it accessible for systems where traditional modeling techniques are ineffective or infeasible. QdFs are used to define the supply rate and storage function, while the data-driven dissipativity conditions derived from these representations are expressed through linear matrix inequalities (LMIs).