On Coercivity and the Frequency Domain Condition in Indefinite LQ-Control

TL;DR

This paper introduces a coercivity condition as a time domain analogue to the frequency domain criterion in indefinite LQ control, linking it to Riccati equation solvability.

Contribution

It presents a novel coercivity condition that characterizes the solvability of Riccati equations in indefinite stochastic LQ control problems.

Findings

Coercivity condition is equivalent to the frequency domain criterion.

Characterizes Riccati equation solvability in stochastic LQ control.

Provides a new time domain perspective on classical frequency conditions.

Abstract

We introduce a coercivity condition as a time domain analogue of the frequency criterion provided by the famous Kalman-Yakubovich-Popov lemma. For a simple stochastic linear quadratic control problem we show how the coercivity condition characterizes the solvability of Riccati equations.