Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization

Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization

[1]  D. J. Newman,et al.  Arithmetic, Geometric Inequality , 1960 .

[2]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[3]  N. Bose,et al.  A quadratic form representation of polynomials of several variables and its applications , 1968 .

[4]  G. Stengle.  A nullstellensatz and a positivstellensatz in semialgebraic geometry , 1974 .

[5]  B. Reznick.  Extremal PSD forms with few terms , 1978 .

[6]  Spyros G. Tzafestas,et al.  Stabilization of singularly perturbed strictly bilinear systems , 1984 .

[7]  John C. Doyle,et al.  Matrix interpolation and H∞ performance bounds , 1985, 1985 American Control Conference.

[8]  M-F Roy,et al.  Géométrie algébrique réelle , 1987 .

[9]  C. Berg.  The multidimensional moment problem and semi-groups , 1987 .

[10]  P. Peres,et al.  a linear programming oriented procedure for quadratic stabilization of uncertain systems , 1989 .

[11]  T. Georgiou,et al.  Optimal robustness in the gap metric , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[12]  A. L. Zelentsovsky.  Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems , 1994, IEEE Trans. Autom. Control..

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  B. Reznick,et al.  Sums of squares of real polynomials , 1995 .

[15]  Olga Taussky-Todd.  SOME CONCRETE ASPECTS OF HILBERT'S 17TH PROBLEM , 1996 .

[16]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[17]  Gilbert Stengle,et al.  Complexity Estimates for the Schmu"dgen Positivstellensatz , 1996, J. Complex..

[18]  V. Powers,et al.  An algorithm for sums of squares of real polynomials , 1998 .

[19]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[20]  Petar V. Kokotovic,et al.  Constructive nonlinear control: Progress in the 90''s , 1999 .

[21]  P. Parrilo,et al.  On convexity in stabilization of nonlinear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[22]  Tor Arne Johansen,et al.  Computation of Lyapunov functions for smooth nonlinear systems using convex optimization , 2000, Autom..

[23]  A. Rantzer.  A dual to Lyapunov's stability theorem , 2001 .

[24]  Constantine Caramanis,et al.  Non-Convex Optimization via Real Algebraic Geometry , 2001 .

[25]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[26]  Pablo A. Parrilo,et al.  Introducing SOSTOOLS: a general purpose sum of squares programming solver , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[27]  A. Papachristodoulou,et al.  On the construction of Lyapunov functions using the sum of squares decomposition , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[28]  Pablo A. Parrilo,et al.  Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..

[29]  Didier Henrion,et al.  GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi , 2003, TOMS.

[30]  D. Kamenetsky.  Symmetry Groups , 2003 .

[31]  Ryan Feeley,et al.  Some controls applications of sum of squares programming , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[32]  P. Parrilo,et al.  Symmetry groups, semidefinite programs, and sums of squares , 2002, math/0211450.

[33]  Gary J. Balas,et al.  Control with disturbance preview and online optimization , 2004, IEEE Transactions on Automatic Control.