An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

Shahzad, Amir; Jones, Bernard J. T.; Kerrigan, Eric C.; Constantinides, George A.

doi:10.1016/j.automatica.2010.10.038

Cited by 39 publications

(30 citation statements)

References 7 publications

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“…Furthermore, this final step of projecting from descriptor to standard state space form can be performed efficiently via a numerical method (Schön et al 2003;Gerdin 2006;Shahzad et al 2011). This is summarised in Appendix B, and has been applied successfully to the problem of flow field estimation in a non-parallel boundary layer ).…”

Section: Dealing With Descriptor Systems: Eliminating the Incompressimentioning

confidence: 99%

Modelling for robust feedback control of fluid flows

et al. 2015

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This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H ∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl's theory of sheared turbulence. To illustrate the application of these techniques, a H ∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall-shear stress in plane channel flow. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller.

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Section: Dealing With Descriptor Systems: Eliminating the Incompressimentioning

confidence: 99%

Modelling for robust feedback control of fluid flows

et al. 2015

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“…The system (11) is an example of a descriptor state-space system (also known as a singular, implicit or generalised state-space system), the control and estimation of which are still an open research field. In this section an algorithm is summarised for converting (11) into a standard state-space system (Schön et al 2003, Gerdin 2006, Shahzad et al 2011.…”

Section: Dealing With Descriptor Systemsmentioning

confidence: 99%

“…The matrices in (13) are computed as follows (Gerdin 2006, Schön et al 2003, Shahzad et al 2011 (i) Compute the generalised Schur form of the matrix pencil λ E D − A D so that:…”

Section: 3) If the Pair (Ementioning

confidence: 99%

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Flow estimation of boundary layers using DNS-based wall shear information

Jones

Kerrigan

Morrison

et al. 2011

International Journal of Control

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This paper investigates the problem of obtaining a state-space model of the disturbance evolution that precedes turbulent flow across aerodynamic surfaces. This problem is challenging since the flow is governed by nonlinear, partial differential-algebraic equations for which there currently exists no efficient controller/estimator synthesis techniques. A sequence of model approximations is employed to yield a linear, low-order state-space model, to which standard tools of control theory can be applied. One of the novelties of this paper is the application of an algorithm that converts a system of differential-algebraic equations into one of ordinary differential equations. This enables straightforward satisfaction of boundary conditions whilst dispensing with the need for parallel flow approximations and velocity-vorticity transformations. The efficacy of the model is demonstrated by the synthesis of a Kalman filter that clearly reconstructs the characteristic features of the flow, using only wall velocity gradient information obtained from a high-fidelity nonlinear simulation.

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“…Many papers have presented different approaches for several matrix equations [7-9, 12-14, 17, 19, 20]. Especially, many problems in control theory can be transformed into the Sylvester matrix equations, such as singular system control [4,21], robust control [3,26], neural network [25,36]. The solvability of linear equations is a fundamental problem, and various results are developed, such as solvability conditions of linear equations for matrices over the complex field [1,2,10,11,18,22,23,[29][30][31][32][33][34]37], solvability conditions of linear equations over algebras or rings [5,6,24,27,28,35].…”

Section: Introductionmentioning

confidence: 99%

Solvability conditions for mixed sylvester equations in rings

Chen

Wang

2017

Filomat

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This paper has been motivated by Wang and He [Q.W. Wang and Z.H. He, Solvability conditions and general solution for mixed Sylvester equations. Automatica, 49 (2013) 2713-2719] in which the authors consider some solvability conditions for mixed Sylvester matrix equations. The paper also considers the same problem in the setting of a regular ring. Using the purely algebraic technique, we present some necessary and sufficient conditions for the solvability to mixed Sylvester equations in rings.

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An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

Cited by 39 publications

References 7 publications

Modelling for robust feedback control of fluid flows

Modelling for robust feedback control of fluid flows

Flow estimation of boundary layers using DNS-based wall shear information

Solvability conditions for mixed sylvester equations in rings

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