Journal ArticleDOI
Robust eigenstructure assignment in quadratic matrix polynomials: Nonsingular case
Nancy Nichols,Jaroslav Kautsky +1 more
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New sensitivity measures, or condition numbers, are derived for the eigenvalues of the quadratic matrix polynomial and a measure of the robustness of the corresponding system is defined that can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations.Abstract:
Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.read more
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The Quadratic Eigenvalue Problem
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SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
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TL;DR: Numerical examples demonstrate that the SOAR method outperforms convergence behaviors of the Krylov subspace--based Arnoldi method applied to the linearized QEP.
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Inverse eigenvalue problems in vibration absorption: Passive modification and active control
TL;DR: In this paper, the state of the art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples, including structural modification by passive elements and active control.
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Parametric eigenstructure assignment in second-order descriptor linear systems
TL;DR: Two complete parametric methods for the proposed eigenstructure assignment problem are presented and both give simple completeParametric expressions for the feedback gains and the closed-loop eigenvector matrices.
Journal ArticleDOI
Analysis and Synthesis of Robust Control Systems Using Linear Parameter Dependent Lyapunov Functions
Jose C. Geromel,R.H. Korogui +1 more
TL;DR: This note provides sufficient robust stability conditions for continuous time polytopic systems from the Frobenius-Perron Theorem applied to the time derivative of a linear parameter dependent Lyapunov function and are expressed in terms of linear matrix inequalities (LMI).
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