Optimization and pole assignment in control system design (Q2738556)

Given a self-conjugate collection \(\Lambda=\{\lambda_1,\dots,\lambda_n\}\) of complex numbers, the pole assignment problem for the controllable pair \((A,B)\in \mathbb{R}^{n\times n}\times \mathbb{R}^{n\times m}\) is to find a gain matrix \(K\in \mathbb{R}^{m\times n}\) such that the spectrum of the closed-loop system matrix \(A+BK\) is \(\Lambda\). In some cases there are several solutions. The author presents a survey of some of the methods for exploiting the freedom in the gain matrix in order to achieve other design objectives. In particular the methods of Kautsky-Nichols-Van Dooren, Byers-Nash and Yang-Tits are considered. A modification of the latter method is also proposed. It must be stressed that to apply the above methods it is necessary to assume that the matrix \(A+BK\) has \(n\) linearly independent eigenvectors and this implicitly implies some restrictions on \(\Lambda\).NEWLINENEWLINEFor the entire collection see [Zbl 0963.00027].