Stabilizability of linear systems with discrete observation mode

TL;DR

This paper investigates the stabilizability of linear control systems under discrete observation modes, characterizing it through weak observability inequalities and comparing it to continuous observation stabilizability.

Contribution

It introduces a novel characterization of stabilizability with discrete observations using weak observability inequalities and explores its relation to continuous observation stabilizability.

Findings

Characterization of stabilizability via weak observability inequalities.

Connections established between discrete and continuous observation stabilizability.

Applications demonstrated for weak observability inequalities.

Abstract

For linear control systems, the usual state feedback stabilizability has two components: one is a continuous observation mode (i.e., to observe solutions continuously in time), and the other is a class of feedback laws (which is usually the space of all of the linear and bounded operators from a state space to a control space). This paper studies the stabilizability for abstract linear control systems, with a discrete observation mode (i.e., to observe solutions discretely in time) and two different classes of feedback laws. We first characterize these types of stabilizabilities via some weak observability inequalities for the dual systems. Then, we use these characterizations to reveal the connections between these types of stabilizabilities and those with continuous observation mode. Finally, we show some applications of the aforementioned weak observability inequalities.