An Analysis of the Pole Placement Problem . I . the Single - Input Case ∗
نویسندگان
چکیده
For the solution of the single-input pole placement problem we derive explicit expressions for the feedback gain matrix as well as the eigenvector matrix of the closed-loop system. Based on these formulas we study the conditioning of the pole-placement problem in terms of perturbations in the data and show how the conditioning depends on the condition number of the closed loop eigenvector matrix, which is a similar to a generalized Cauchy matrix, the norm of the feedback vector and the distance to uncontrollability.
منابع مشابه
Adaptive fuzzy pole placement for stabilization of non-linear systems
A new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. We use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. Then, we linearized this identified model at each sampling time to have an approximate linear time varying system. In order to stabilize...
متن کاملPole placement algorithm for control of civil structures subjected to earthquake excitation
In this paper the control algorithm for controlled civil structures subjected to earthquake excitation is thoroughly investigated. The objective of this work is the control of structures by means of the pole placement algorithm, in order to improve their response against earthquake actions. Successful application of the algorithm requires judicious placement of the closed-loop eigenvalues from ...
متن کاملAn Analysis of the Pole Placement Problem Ii. the Multi-input Case∗
For the solution of the multi-input pole placement problem we derive explicit formulas for the subspace from which the feedback gain matrix can be chosen and for the feedback gain as well as the eigenvector matrix of the closed-loop system. We discuss which Jordan structures can be assigned and also when diagonalizability can be achieved. Based on these formulas we study the conditioning of the...
متن کاملChoosing Poles so That the Single-input Pole Placement Problem Is Well Conditioned∗
We discuss the single-input pole placement problem (SIPP) and analyze how the conditioning of the problem can be estimated and improved if the poles are allowed to vary in specific regions in the complex plane. Under certain assumptions we give formulas as well as bounds for the norm of the feedback gain and the condition number of the closed loop matrix. Via several numerical examples we demon...
متن کاملDirect algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case
This paper deals with the direct solution of the pole placement problem by statederivative feedback for multi-input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure resu...
متن کامل