Analysis and design of dynamic systems via the Lyapunov theorem and the invariance principle of LaSalle

Abstract

The objective of this research project is the study of design and stability analysis methods for dynamical systems. The theory to be used is based on the construction of Lyapunov functions which result in analysis and synthesis conditions described mainly in terms of linear matrix inequalities (LMIs). In order to embrace more cases than the ones assured by the Lyapunov theorem, it will also be analysed Lyapunov functions with time derivative equal to zero, or even positive, based on the invariance principle of LaSalle and its extensions. Specifically, issues that will be addressed: stability analysis of switched systems, stability analysis and estimation of the region of attraction of multilinear systems (bilinear, etc.) and synthesis of reduced order controllers for bilinear systems.