Symmetry preserving partial pole assignment for the standard and the generalized eigenvalue problems

Abstract

Many real-life state feedback control systems are modelled by a set of single-input, time-invariant linear equations. Often, these lead to a pair of matrices which are real and symmetric. The pole assignment problem requires us to find a state feedback control which gives the closed loop matrices a prescribed set of poles. Commonly used controls produce a closed loop matrix which is no longer symmetric. In this paper we present an explicit solution for a new symmetry preserving partial pole assignment method for the generalized eigenvalue problem and for the standard eigenvalue problem. The methods are demonstrated on illustrative examples and can produce computationally accurate solutions for even quite large systems.