Stabilizability and Detectability

Abstract

One of the most important concepts of systems theory is that of stabilizability and its dual concept detectability. We characterise when a system with finitely many inputs is stabilizable. Additionally, we present tests for the stabilizability/detectability of spatially invariant, Riesz-spectral, and delay systems. Similar as for finite-dimensional systems, we show that a system can be stabilized by a dynamic compensator provided it is stabilizable and detectable. As shown in the charactrization of stabilizability, exponential stabilzability may be impossible for certain classes of systems, such as collocated systems. Therefor we also characterize the weaker concept of strong stabilizability. The chapter ends with a set of 21 exercises and a notes and references section.