Local stability analysis using simulations and sum-of-squares programming

[1]  A. Packard,et al.  Stability region analysis using sum of squares programming , 2006, 2006 American Control Conference.

[2]  B. Tibken,et al.  Computing the domain of attraction for polynomial systems via BMI optimization method , 2006, 2006 American Control Conference.

[3]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[4]  Weehong Tan,et al.  Nonlinear Control Analysis and Synthesis using Sum-of-Squares Programming , 2006 .

[5]  A. Garulli,et al.  LMI‐based computation of optimal quadratic Lyapunov functions for odd polynomial systems , 2005 .

[6]  A. Papachristodoulou Scalable analysis of nonlinear systems using convex optimization , 2005 .

[7]  G. Serpen Search for A Lyapunov Function through Empirical Approximation by Artificial Neural Nets : Theoretical Framework , 2005 .

[8]  B. Yegnanarayana,et al.  Artificial Neural Networks , 2004 .

[9]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

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

[11]  O. Hachicho,et al.  Estimating domains of attraction of a class of nonlinear dynamical systems with LMI methods based on the theory of moments , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  B. Tibken Estimation of the domain of attraction for polynomial systems via LMIs , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[13]  Danil V. Prokhorov,et al.  Application of SVM to Lyapunov function approximation , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[14]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[15]  O. Toker,et al.  On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[16]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

[17]  J. Hauser,et al.  Estimating Quadratic Stability Domains by Nonsmooth Optimization , 1992, 1992 American Control Conference.

[18]  J. Thorp,et al.  Stability regions of nonlinear dynamical systems: a constructive methodology , 1989 .

[19]  A. Vicino,et al.  On the estimation of asymptotic stability regions: State of the art and new proposals , 1985 .

[20]  Mathukumalli Vidyasagar,et al.  Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems , 1981, Autom..

[21]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[22]  E. Davison,et al.  A computational method for determining quadratic lyapunov functions for non-linear systems , 1971 .

[23]  Davison,et al.  A computational method for determining quadratic Lyapunov Functions for nonlinear systems , 1970 .