Transient Effects of Linear Dynamical Systems

This work discusses the behavior of linear continuous-time dynamical systems on small and medium-sized time-scales, i.e., before asymptotic effects rule the system's behavior.A general theoretical framework is established in this work. Some special cases are studied, in particular, time-delay systems and positive systems. These studies give rise to certain Lyapunov-functionswhich can be used to estimate the transient behavior of the system.The synthesis of feedback-controllers which satify certain given transientbounds is also considered