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Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53060#.VLSMVMnQrzE Author(s) Şerife Yılmaz , Taner Büyükköroğlu , Vakif Dzhafarov Affiliation(s) Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey . ABSTRACT Asymptotic stability of linear systems is closely related to Hurwitz stability of the system matrices. For uncertain linear systems we consider stability problem through common quadratic Lyapunov functions (CQLF) and problem of stabilization by linear feedback.   KEYWORDS Common Quadratic Lyapunov Functions , Uncertain System , Gradient Method , Bendixson Theorem Cite this paper Yılmaz, Ş. , Büyükköroğlu, T. and Dzhafarov, V. (2015) On Asymptotic Stability of Linear Control Systems. Applied Mathematics , 6 , 71-77. doi: 10.4236/am.2015.61008 .   References [ 1 ] Liberzon, D. (2003) Switching in System and Control. Birkhäuser, Boston. http://dx.doi.org/10.1007/97...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50894#.VE8GxFfHRK0 Author(s)   Heredia Ramírez Francisco Andrés , Johann Hernandez , Edwin Rivas Trujillo Affiliation(s) Universidad Distrital Francisco José de Caldas, Bogotá, Colombia . ABSTRACT This paper presents in the first place, the state of art relating to the methods to solve optimal power flows (OPF) and its application in electrical microgrids. Afterwards, a mathematical algorithm based on the gradient method is proposed for the application of OPF in a low power microgrid, in order to improve the voltages profiles and consequently reduce the active power losses. Finally, the proposed algorithm is implemented in a...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50346#.VDskCVfHRK1 Author(s)     Şerife Yılmaz , Taner Büyükköroğlu Affiliation(s) Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey . ABSTRACT We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and give a new sufficient condition for the second problem. A number of examples are considered. KEYWORDS Stable Matrix , Matrix Family , Common Quadratic Lyapunov Functions , Switched System , Gradient...