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Sum-of-Squares Applications in Nonlinear Controller Synthesis

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REFERENCESREFERENCESReferences[1] Artste<strong>in</strong>, Z.: Stabilization with Relaxed Controls. In: Nonl<strong>in</strong>ear Analysis, Theory,Methods & <strong>Applications</strong> 7 (1983), No. 11, pp. 1163–1173[2] Balas, G. ; Packard, A. ; Seiler, P. ; Topcu, U.: Robustness Analysis <strong>of</strong> Nonl<strong>in</strong>earSystems. 2009. – Available at http://www.aem.umn.edu/~AerospaceControl/[3] Bochnak, J. ; Coste, M. ; Roy, M.-F.: Real Algebraic Geometry. Berl<strong>in</strong> : Spr<strong>in</strong>ger,1991[4] Boyd, S. ; El Ghaoui, L. ; Feron, E. ; Balakrishnan, V.: L<strong>in</strong>ear Matrix Inequalities<strong>in</strong> System and Control Theory. SIAM, 1994[5] Choi, M. ; Lam, T. ; Reznick, B.: <strong>Sum</strong>s <strong>of</strong> <strong>Squares</strong> <strong>of</strong> Real Polynomials. In: Proceded<strong>in</strong>gs<strong>of</strong> Symposia <strong>in</strong> Pure Matematics Vol. 58, 1995, pp. 103–126[6] Freeman, R. A. ; Kokotovic, P. V.: Robust Nonl<strong>in</strong>ear Control Design: State-Spaceand Lyapunov Techniques. 1st ed. Birkhäuser Boston, 1996[7] Freeman, R. A. ; Primbs, J. A.: Control Lyapunov Functions: New Ideas from an oldSource. In: Decision and Control, 1996., Proceed<strong>in</strong>gs <strong>of</strong> the 35th IEEE Vol. 4, 1996,pp. 3926–3931[8] Isidori, A.: Nonl<strong>in</strong>ear Control Systems. 3rd ed. Spr<strong>in</strong>ger, 1995[9] Jarvis-Wloszek, Z.: Lyapunov Based Analysis and <strong>Controller</strong> <strong>Synthesis</strong> for PolynomialSystems us<strong>in</strong>g <strong>Sum</strong>-<strong>of</strong>-<strong>Squares</strong> Optimization, University <strong>of</strong> California, Berkeley,Ph.D. thesis, 2003[10] Jarvis-Wloszek, Z. ; Feeley, R. ; Tan, W. ; Sun, K. ; Packard, A.: Control<strong>Applications</strong> <strong>of</strong> <strong>Sum</strong> <strong>of</strong> <strong>Squares</strong> Programm<strong>in</strong>g. In: Henrion, D. (Edt.) ; Garulli, A.(Edt.): Positive Polynomials <strong>in</strong> Control. Berl<strong>in</strong> : Spr<strong>in</strong>ger, 2005[11] Kalman, R.: Contributions to the Theory <strong>of</strong> Optimal Control. In: Bolet<strong>in</strong> de laSociedad Matematica Mexicana 5 (1960), pp. 102–119[12] Khalil, H. K.: Nonl<strong>in</strong>ear Systems. 3rd ed. Prentice Hall, 2001[13] Löfberg, J.: YALMIP : A Toolbox for Model<strong>in</strong>g and Optimization <strong>in</strong> MATLAB. In:Proceed<strong>in</strong>gs <strong>of</strong> the CACSD Conference. Taipei, Taiwan, 2004. – Available at http://users.isy.liu.se/johanl/yalmip32

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