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

We provide a set of counterexamples for the monotonicity of the Newton-Hewer method (Hewer, 1971) for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation (Caines and Mayne, 1970). (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The article provides a set of counterexamples to illustrate the monotonicity of the Newton-Hewer method in solving the discrete-time algebraic Riccati equation in dynamic settings, contrasting it with the Riccati difference equation.