Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

Robust pole assignment in linear state feedback

Robust eigenstructure assignment via dynamical compensators

This paper surveys the field of eigenstructure assignment literature from the early 1960s to the present. The eigenstructure assignment problem is first defined as the assignment of eigenvectors within an eigenspace associated with each eigenvalue. Four broad approaches to eigenstructure assignment are identified: the protection method, the parametric method, the projection method and the orthogonal eigenvector method. The major papers for each method are described in a common nomenclature and the techniques discussed. Recent developments such as parameter uncertainty robustness and hybrid eigenstructure assignment/H∞ control are examined in the recent literature, together with some suggestions for future research. The survey includes over 140 important references.

Eigenstructure Assignment: A Survey:

Based on a newly proposed eigenstructure assignment result and the matrix eigenvalue sensitivity theory, a simple effective algorithm for robust pole assignment in multivariable linear systems via output feedback is presented, which gives a robust solution in the sense that the closed-loop eigenvalues are as insensitive as possible to perturbations in the system coefficient matrices. The algorithm does not contain ‘going back’ procedures, and may conveniently include closed-loop eigenvalues as optimising parameters, and also possesses good numerical property and better optimality. Computational results show its effect and simplicity.

Simple algorithm for robust pole assignment in linear output feedback

Algorithms are proposed for eigenvalue assignment (EVA) by constant as well as dynamic output feedback. The main algorithm is developed for single-input, multioutput systems and the results are then extended to multiinput, multioutput systems. In computing the feedback, use is made of the fact that the closed-loop eigenvalues can almost always be assigned arbitrarily close to the desired locations in the complex plane, provided the system satisfies the condition m+p>n, where m, p, and n are , respectively, the number of inputs, outputs and states of the system. The EVA problem has been treated as a converse of the algebraic eigenvalue problem. The proposed algorithms are based on the implicitly shifted QR algorithm for solving the algebraic eigenvalue problem. The performance of the algorithms is illustrated by several numerical examples. >

E K-w Chu

Papers

Robust pole assignment by output feedback

Reliable algorithms for reduced order observer design