On Real Stable Pole Placement for Structured Systems Using Sturm and Sturm-Habicht Sequences

Röbenack, Klaus; Voßwinkel, Rick

doi:10.1016/j.ifacol.2020.12.475

Cited by 2 publications

(3 citation statements)

References 33 publications

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“…see [26]- [28]. Similar conditions can be derived for the stability with purely real eigenvalues, i.e., with roots on the open left half real axis, see [28]- [31].…”

Section: B Stabilitymentioning

confidence: 80%

“…First, we want to compute the gain matrices with the minimum Frobenius norm as well as minimum spectral norm using the Lagrangian functions ( 29) and (33), respectively. From (30) we obtain the polynomials generating the ideals (31). Using SAGEMATH [39], we computed the associated varieties.…”

Section: A Examplementioning

confidence: 99%

“…To minimize the spectral norm, we used the Lagrangian (29) and computed the ideal (31). The associated variety is zero-dimensional and consists of 20 points, of which 8 points correspond to a real gain matrix.…”

Section: Examplementioning

confidence: 99%

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Full and Partial Eigenvalue Placement for Minimum Norm Static Output Feedback Control

Röbenack

Gerbet

2022

Syst. Theor. Control Comput. J.

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The controller design for linear time-invariant state space systems seems to be straightforward and well established. This is not true for static output feedback control, which is still a challenging task. This paper deals with controller design based on eigenvalue assignment. We consider the placement of distinct as well as multiple real eigenvalues or complex conjugate pairs. The desired eigenvalue configurations are characterised in terms of algebraic divisibility of the characteristic polynomial of the closed-loop system. We also consider the problem of partial eigenvalue placement, where not all eigenvalues are fixed by feedback. Degrees of freedom in the controller design are used for the minimization of various matrix norms of the feedback gain matrix.

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“…see [26]- [28]. Similar conditions can be derived for the stability with purely real eigenvalues, i.e., with roots on the open left half real axis, see [28]- [31].…”

Section: B Stabilitymentioning

confidence: 80%

Section: A Examplementioning

confidence: 99%