Switching Strategies for Linear Feedback Stabilization with Sparsified State Measurements

TL;DR

This paper explores stabilization of continuous-time linear systems using sparse state measurements obtained via compressive sampling, analyzing switching strategies among sparsifiers to ensure stability across various system dimensions.

Contribution

It extends previous discrete-time sparse measurement techniques to continuous-time systems and analyzes the impact of switching strategies on system stability.

Findings

Switching among sparsifiers affects stability in continuous systems.

Results generalized from low to arbitrary system dimensions.

Stable control achieved with appropriate switching strategies.

Abstract

In this paper, we address the problem of stabilization in continuous time linear dynamical systems using state feedback when compressive sampling techniques are used for state measurement and reconstruction. In [5], we had introduced the concept of using l1 reconstruction technique, commonly used in sparse data reconstruction, for state measurement and estimation in a discrete time linear system. In this work, we extend the previous scenario to analyse continuous time linear systems. We investigate the effect of switching within a set of sparsifiers, introduced in [5], on the stability of a linear plant in continuous time settings. Initially, we analyze the problem of stabilization in low dimensional systems, following which we generalize the results to address the problem of stabilization in systems of arbitrary dimensions.