On the lack of monotonicity of Newton-Hewer updates for Riccati equations

TL;DR

This paper presents counterexamples showing that the Newton-Hewer method does not always preserve monotonicity when solving discrete-time algebraic Riccati equations, highlighting differences from Riccati difference equations.

Contribution

It introduces counterexamples demonstrating the non-monotonic behavior of the Newton-Hewer method in discrete-time Riccati equations.

Findings

Counterexamples show non-monotonicity of Newton-Hewer updates.

Highlights contrast with Riccati difference equations.

Implications for stability and convergence analysis.

Abstract

We provide a set of counterexamples for the monotonicity of the Newton-Hewer method for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation.