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Original Articles

Robust stabilisation of polynomial systems with uncertain parameters

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Pages 575-584 | Received 13 Jun 2008, Accepted 13 May 2009, Published online: 10 Mar 2010

References

  • Battaini , M and Casciati , F . 1996 . Chaotic Behaviour of Hysteretic Oscillators . Journal of Structural Control , 3 : 7 – 19 .
  • Becker , T and Weispfenning , V . 1993 . Gröbner Bases: A Computational Approach to Commutative Algebra , New York : Springer .
  • Boyd , S , El Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . Linear Matrix Inequalities in System and Control Theory , Philadephia : Society for Industrial and Applied Mathematics .
  • Dang , T . 2006 . Approximate Reachability Computation for Polynomial Systems . Lecture Notes in Computer Science , 3927 : 138 – 152 .
  • El-Samad , H , Prajna , S , Papachristodoulou , A , Doyle , J and Khammash , M . 2006 . Advanced Methods and Algorithms for Biological Networks Analysis . Proceedings of the IEEE , 94 ( 4 ) : 832 – 853 .
  • Guckenheimer , J and Holmes , P . 1983 . Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , New York : Springer .
  • Henrion , D and Lasserre , JB . 2004 . Solving Nonconvex Optimization Problems . IEEE Control Systems Magazine , 24 : 72 – 83 .
  • Henrion , D and Lasserre , JB . 2006 . Convergent Relaxations of Polynomial Matrix Inequalities and Static output Feedback . IEEE Transactions on Automatic Control , 51 ( 2 ) : 192 – 202 .
  • Hong , J and Bernstein , DS . 2001 . Adaptive Stabilization of Nonlinear Oscillators Using Direct Adaptive Control . International Journal of Control , 74 ( 5 ) : 432 – 444 .
  • Isidori , A . 1995 . Nonlinear Control Systems , New York : Springer .
  • Krstić , M , Kanellakopoulos , I and Kokotović , P . 1995 . Nonlinear and Adaptive Control Design , New York : John Wiley & Sons, Inc .
  • Lasserre , JB . 2001 . Global Optimization with Polynomials and the Problem of Moments . SIAM Journal on Optimization , 11 : 796 – 817 .
  • Masri , SF and Caughey , TK . 1979 . A Nonparametric Identification Technique for Nonlinear Dynamic Problems . ASME Journal of Applied Mechanics , 46 : 433 – 447 .
  • Moon , FC and Holmes , PJ . 1979 . A Magnetoelastic Strange Attractor . Journal of Sound and Vibration , 65 : 285 – 296 .
  • Orlov , Y , Aguilar , L , Acho , L and Ortiz , A . 2008 . Asymptotic Harmonic Generator and its Application to Finite time Orbital Stabilization of a Friction Pendulum with Experimental Verification . International Journal of Control , 81 ( 2 ) : 227 – 234 .
  • Papachristodoulou , A and Prajna , S . On the Construction of Lyapunov Functions Using the Sum of Squares Decomposition . Proceedings of the 41st Conference on Decision and Control . December 2002 . pp. 3482 – 3487 . Las Vegas, Nevada, , USA
  • Parrilo , PA . 2000 . “ Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization ” . In PhD thesis , Pasadena, California, , USA : California Institute of Technology .
  • Pozo , F . 2005 . “ Nonlinear Control of Uncertain System: Some Application-oriented Issues ” . In PhD thesis , Barcelona, , Spain : Universitat Politécnica de Catalunya .
  • Pozo , F , Ikhouane , F and Rodellar , J . 2005 . “ Control Synthesis of Systems with Uncertain Parameters by Convex Optimization ” . In Proceedings of the 16th IFAC World Congress Prague, , Czech Republic July. Available online at http://www.ifac-papersonline.net/
  • Prajna , S , Papachristodoulou , A and Parrilo , PA . Introducing SOSTOOLS: A General Purpose Sum of Squares Programming Solver . Proceedings of the 41st Conference on Decision and Control . December 2002 . pp. 741 – 746 . Las Vegas, Nevada, , USA
  • Prajna , S , Parrilo , PA and Rantzer , A . 2004a . Nonlinear Control Synthesis by Convex Optimization . IEEE Transactions on Automatic Control , 49 ( 2 ) : 310 – 314 .
  • Prajna , S , Papachristodoulou , A , Seiler , P and Parrilo , PA . New Developments in Sum of Squares Optimization and SOSTOOLS . Proceedings of the 2004 American Control Conference . July 2004b . pp. 5606 – 5611 . Boston, Massachusetts, , USA
  • Prajna , S , Papachristodoulou , A and Wu , F . Nonlinear Control Synthesis by Sum of Squares Optimization: A Lyapunov-based Approach . Proceedings of the 5th Asian Control Conference . July 2004c . pp. 157 – 165 . Melbourne, , Australia
  • Prestel , A and Delzell , CN . 2001 . Positive Polynomials. From Hilbert 17th's Problem to Real Algebra , New York : Springer .
  • Prieur , C and Praly , L . Uniting Local and Global Controllers . Proceedings of the 38th Conference on Decision and Control . December 1999 . pp. 1214 – 1219 . Phoenix, Arizona, , USA
  • Putinar , M . 1993 . Positive Polynomials on Compact Semi-algebraic Sets . Indiana University Mathematical Journal , 42 ( 3 ) : 969 – 984 .
  • Rantzer , A . 2001 . A dual to Lyapunov's Stability Theorem . Systems and Control Letters , 42 : 161 – 168 .
  • Samadi , B and Rodrigues , L . 2008 . Extension of Local Linear Controllers to Global Piecewise Affine Controllers for Uncertain Non-linear Systems . International Journal of Systems Science , 39 ( 9 ) : 867 – 879 .
  • Stengle , G . 1974 . A Nullstellensatz and a Positivstellensatz in Semialgebraic Geometry . Mathematische Annalen , 207 : 87 – 97 .
  • Wolfe , RW , Masri , SF and Caffrey , J . 2002 . Some Structural Health Monitoring Approaches for Nonlinear Hydraulic Dampers . Journal of Structural Control , 9 : 5 – 18 .

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