Solving polynomial static output feedback problems with PENBMI

Henrion, Didier; Löfberg, Johan; Kočvara, Michal; Stingl, Michael

doi:10.1109/cdc.2005.1583385

Cited by 107 publications

(94 citation statements)

References 13 publications

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“…. , m, this function computes the coefficients of the multivariate polynomial p(z) = det(H 0 + H 1 z 1 + · · · + H m z m ); it proceeds by sampling and interpolation, as described in [12] • trigoherm.m -computes the Hermite matrix of a homogenized multivariate polynomial; it uses the formula of [3,Theorem 3.13] adapted to complex coefficients…”

Section: Examplesmentioning

confidence: 99%

Positive trigonometric polynomials for strong stability of difference equations

Henrion¹,

Vyhlídal²

2011

IFAC Proceedings Volumes

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We follow a polynomial approach to analyse strong stability of continuous-time linear difference equations with several delays Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial, assessing strong stability amounts to deciding positive definiteness of a multivariate trigonometric polynomial matrix. This latter problem is addressed with a converging hierarchy of linear matrix inequalities (LMIs). Numerical experiments indicate that certificates of strong stability can be obtained at a reasonable computational cost for state dimension and number of delays not exceeding 4 or 5.

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Section: Examplesmentioning

confidence: 99%

Positive trigonometric polynomials for strong stability of difference equations

Henrion¹,

Vyhlídal²

2011

IFAC Proceedings Volumes

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“…Assume that K (0) ∈ int (S α ) was found by the RS algorithm (see [16]) or by any other method (see [19][20][21]). Let h > 0 and let U (0) be a unit vector w.r.t.…”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

Peretz¹

2018

Algorithms

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Abstract:In this article we suggest a randomized algorithm for the LQR (Linear Quadratic Regulator) optimal-control problem via static-output-feedback. The suggested algorithm is based on the recently introduced randomized optimization method called the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The algorithm presented here is a randomized algorithm with a proof of convergence in probability. Its practical implementation has good performance in terms of the quality of controllers obtained and the percentage of success.

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“…Therefore, (38) can be used for robust controller design either directly -using appropriate BMI solver (Henrion et al, 2005) or using some convexifying approach, (for discrete-time case see e.g. (Crusius & Trofino, 1999;deOliveira et al, 1999)).…”

Section: Corollary 31mentioning

confidence: 99%