A Continuation Approach to Global Eigenvalue Assignment

Abstract

This paper describes an alternative approach to global eigenvalue assignment called a continuation method. The method is a homotopy technique which embeds the global control problem into a parameterized family of global control problems. This parameterization describes a continuous deformation of a system with the desired spectrum into the original system. Based on this deformation, a differential equation is constructed whose solution trajectory has an endpoint which is a constant output feedback matrix assigning the desired spectrum to the original system.The development of this differential equation and conditions that guarantee the existence of a solution are given. Also, two examples of its numerical implementation are detailed.