Inexact Newton and quasi-Newton methods for the output feedback pole assignment problem

The pole assignment problem (PAP) is a special algebraic inverse eigenvalue problem. In this paper, we present two types of algorithms, namely a quasi-Newton method with line search and some variants of the inexact Newton methods to tackle that problem. For a nonmonotone version of inexact Newton–Krylov method, we give local convergence under the assumptions of semismoothness and BD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BD$$\end{document}-regularity at the solution and global convergence under a nonmonotonic backtracking strategy. For a quasi-Newton method with line search, under suitable assumptions, we show local Q-superlinear convergence. Also, we consider a proximal point quasi-Newton algorithm for solving PAP. Moreover, we modify these methods to tackle the PAP where the corresponding control system is with time delay. Numerical results illustrate the performance of the proposed methods.