The infinite-dimensional dissipation inequality

TL;DR

This paper investigates the dissipativity of linear infinite-dimensional systems using operator inequalities, providing insights into their dissipation rates and implications for linear-quadratic optimal control problems.

Contribution

It introduces a characterization of dissipativity via operator inequalities for infinite-dimensional systems, linking it to dissipation rates and control problem implications.

Findings

Characterization of dissipativity through operator inequalities.

Derivation of dissipation rates for infinite-dimensional systems.

Implications for linear-quadratic optimal control on half-line.

Abstract

We study the dissipativity of linear infinite-dimensional systems with respect to a prescribed quadratic supply rate functional. We characterize this property via an operator inequality that also yields the system's dissipation rate. We also derive implications for the linear-quadratic optimal control problem on the nonnegative real half-line.