2,660 research outputs found
Plane geometry and convexity of polynomial stability regions
The set of controllers stabilizing a linear system is generally non-convex in
the parameter space. In the case of two-parameter controller design (e.g. PI
control or static output feedback with one input and two outputs), we observe
however that quite often for benchmark problem instances, the set of
stabilizing controllers seems to be convex. In this note we use elementary
techniques from real algebraic geometry (resultants and Bezoutian matrices) to
explain this phenomenon. As a byproduct, we derive a convex linear matrix
inequality (LMI) formulation of two-parameter fixed-order controller design
problem, when possible
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A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
Discretization of Navier--Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(hk+1/2) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization
A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
Discretization of Navier-Stokes' equations using pressure-robust finite
element methods is considered for the high Reynolds number regime. To counter
oscillations due to dominating convection we add a stabilization based on a
bulk term in the form of a residual-based least squares stabilization of the
vorticity equation supplemented by a penalty term on (certain components of)
the gradient jump over the elements faces. Since the stabilization is based on
the vorticity equation, it is independent of the pressure gradients, which
makes it pressure-robust. Thus, we prove pressure-independent error estimates
in the linearized case, known as Oseen's problem. In fact, we prove an
error estimate in the -norm that is known to be the
best that can be expected for this type of problem. Numerical examples are
provided that, in addition to confirming the theoretical results, show that the
present method compares favorably to the classical residual-based SUPG
stabilization
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Efficient Reorientation Maneuvers for Spacecraft with Multiple Articulated Payloads
A final report is provided which describes the research program during the period 3 Mar. 1992 to 3 Jun. 1993. A summary of the technical research questions that were studied and of the main results that were obtained is given. The specific outcomes of the research program, including both educational impacts as well as research publications, are listed. The research is concerned with efficient reorientation maneuvers for spacecraft with multiple articulated payloads
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