Characterization by detectability inequality for periodic stabilization of linear time-periodic evolution systems

TL;DR

This paper introduces a new way to characterize the periodic stabilization of linear time-periodic systems using detectability inequalities, extending previous results from time-invariant systems to periodic ones.

Contribution

It provides a novel characterization of periodic stabilization for linear time-periodic systems via detectability inequalities, generalizing existing observability-based methods.

Findings

Characterization of periodic stabilization using detectability inequalities

Extension of time-invariant system results to time-periodic systems

Theoretical framework applicable to Hilbert space control systems

Abstract

Given a linear time-periodic control system in a Hilbert space with a bounded control operator, we present a characterization of periodic stabilization in terms of a detectability inequality. Similar characterizationwas built up in [E. Trelat, G. Wang, Y. Xu, Characterization by observability inequalities of controllability and stabilization properties, Pure and Appl. Anal., 2 (2020), 93-122] for time-invariant systems.