PhD defence | Peter Stechlinski, Qualitative Theory of Switched Integro-differential Equations with Applications

Qualitative Theory of Switched Integro-differential Equations with Applications

Many real-world phenomena found in branches of applied math, computer science, and engineering are naturally modelled by hybrid systems. Switched systems, which are a type of hybrid system, evolve according to mode-dependent continuous dynamics and experience abrupt changes between modes based on a switching rule. The main focus of the present thesis is on studying the qualitative behaviour of switched integro-differential systems with impulses. In order to ensure the models are well-posed, some fundamental theory is developed. A stability analysis is performed by extending the current theoretical approaches in the switched systems literature. Contributions are made to hybrid control theory by extending current results on stabilization by state-dependent switching and impulsive control. The analytic results found are applied to epidemic models with time-varying parameters (for example, a seasonal model of Chikungunya disease and a general vector-borne disease model).