PSEUDOSPECTRAL METHODS FOR ROBUST STABILIZATION OF LINEAR SYSTEMS

The theory of pseudospectra for linear maps has a wide range of applications in various fields, such as numerical linear algebra, fluid dynamics, quantum mechanics, and is receiving increasing attention in control theory. In control applications, pseudospectra are typically linked to the analysis of a system’s transient behaviour. Here, by building on the fact that one of their equivalent definitions relies on bounded matrix perturbations, they are employed as a design tool for robust stabilization. This thesis first introduces the theoretical aspects of pseudospectra and next exploits the analysis of a matrix’s pseudospectrum in ensuring robust stability against bounded unstructured perturbations These new theoretical notions lay the groundwork for an algorithm that robustly stabilizes both continuous- and discrete-time linear systems.