. . . "2008-07-20+02:00"^^ . "386732" . . . . "Henrion, Didier" . . . "Association of Computing Machinery" . "21230" . "Proceedings of the International Symposium on Symbolic and Algebraic Computations" . "RIV/68407700:21230/08:03145471!RIV09-MSM-21230___" . "P(GA102/08/0186), Z(MSM6840770038)" . "RIV/68407700:21230/08:03145471" . "Geometrie roviny a konvexita polynomi\u00E1ln\u00EDch oblast\u00ED stability"@cs . . . "Geometrie roviny a konvexita polynomi\u00E1ln\u00EDch oblast\u00ED stability"@cs . . . "6"^^ . "control theory; convexity; resultants"@en . "2"^^ . . . "2"^^ . "Hagenberg" . "New York" . . "[C1371E583392]" . . . "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 B\u00B4ezoutian 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."@en . "Plane geometry and convexity of polynomial stability regions" . "Plane geometry and convexity of polynomial stability regions"@en . "\u0160ebek, Michael" . "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 B\u00B4ezoutian 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." . "Plane geometry and convexity of polynomial stability regions"@en . "Geometrie roviny a konvexita polynomi\u00E1ln\u00EDch oblast\u00ED stability"@cs . "Plane geometry and convexity of polynomial stability regions" . . "978-1-59593-904-3" . .