Time-domain performance based non-linear state feedback control of constrained linear systems

References

• Asseo , S . 1969 . Optimal Control of a Servo Derived from Nonquadratic Performance Criteria . IEEE Transactions on Automatic Control , 14 : 404 – 407 .
   Google Scholar
• Bass , R and Webber , R . 1966 . Optimal Non-linear Feedback Control Derived from Quartic and Higher-order Performance Criteria . IEEE Transactions on Automatic Control , 11 : 448 – 454 .
   Web of Science ®Google Scholar
• Bemporad , A , Casavola , A and Mosca , E . 1997 . Nonlinear Control of Constrained Linear Systems via Predictive Reference Management . IEEE Transactions on Automatic Control , 42 : 340 – 349 .
   Web of Science ®Google Scholar
• Bernstein , D . 1991 . “ Nonquadratic Cost and Non-linear Feedback Control ” . In in IEEE ACC 533 – 538 . Boston
   Google Scholar
• Bhat , S and Miu , D . 1990 . Precise Point-to-point Positioning Control of Flexible Structures . Journal of Dynamic Systems Measurement and Control , 112 : 667 – 674 .
   Google Scholar
• Bode , H . 1945 . Network Analysis and Feedback Amplifier Design , New York : D. van Nostrand .
   Google Scholar
• Boyd , S and Barratt , C . 1991 . Linear Controller Design: Limits of Performance , New Jersey : Prentice Hall .
   Google Scholar
• Haddad , W , Chellaboina , VS and Fausz , J . 1998 . Robust Non-linear Feedback Control for Uncertain Linear Systems with Nonquadratic Performance Criteria . System & Control Letters , 33 : 327 – 338 .
   Google Scholar
• Heertjes , M and Steinbuch , M . 2004 . Stability and Performance of a Variable Gain Controller with Application to a Dvd Storage Drive . Automatica , 40 : 591 – 602 .
   Google Scholar
• Henrion , D and Lasserre , JB . 2006 . LMIs for Constrained Polynomial Interpolation with Application in Trajectory Planning . System & Control Letters , 55 : 473 – 477 .
   Web of Science ®Google Scholar
• Henrion , D , Tarbouriech , S and Kucera , V . 2005 . Control of Linear Systems Subject to Time-domain Constraints with Polynomial Pole Placement and LMIs . IEEE Transactions on Automatic Control , 50 : 1360 – 1364 .
   Google Scholar
• Khalil , H . 1992 . Nonlinear Systems , New York : MacMillan .
   Google Scholar
• Kreyzig , E . 1978 . Introductory Functional Analysis with Applications , New York : John Wiley & Sons .
   Google Scholar
• Levine , J and Nguyen , D . 2003 . Flat Output Characterisation for Linear Systems using Polynomial Matrices . System & Control Letters , 48 : 69 – 75 .
   Web of Science ®Google Scholar
• Löfberg , J . YALMIP: A Toolbox for Modeling and Optimization in MATLAB . Proceedings in CACSD Conference . Taipei, , Taiwan
   Google Scholar
• PolyX Ltd. 2001 . The Polynomial Toolbox for Matlab , Prague : Czech Republic .
   Google Scholar
• Mayne , D , Rawlings , J , Rao , C and Scokaert , P . 2000 . Constrained Model Predictive Control: Stability and Optimality . Automatica , 36 : 789 – 814 .
   Web of Science ®Google Scholar
• Moylan , P and Anderson , B . 1973 . Nonlinear Regulator Theory and an Inverse Optimal Control Problem . IEEE Transactions on Automatic Control , 18 : 460 – 465 .
   Web of Science ®Google Scholar
• Papachristodoulou , A . 2005 . “ Scalable analysis of Non-linear Systems using Convex Optimisation ” . In PhD thesis , Pasadena, CA : California Institute of Technology .
   Google Scholar
• Papachristodoulou , A and Prajna , S . 2005 . A Tutorial on Sum of Squares Techniques for Systems Analysis . IEEE ACC , 4 : 2686 – 2700 .
   Google Scholar
• Parrilo , P . 2000 . “ Structured Semidefinte Programs and Semialgebraic Geometry Methods in Robustness and Optimisation ” . In PhD thesis , Pasadena, CA : California Institute of Technology .
   Google Scholar
• Prajna , S , Papachristodoulou , A and Parrilo , P . 2002a . Introducing SOSTOOLS: A General Purpose Sum of Squares Programming Solver . IEEE conference on Decision and Control , 1 : 741 – 746 .
   Google Scholar
• Prajna , S , Papachristodoulou , A and Parrilo , P . 2002b . SOSTOOLS–Sum-of-squares Optimisation toolbox for MATLAB, User's Guide , Pasadena : California Institute of Technology .
   Google Scholar
• Rekasius , Z . 1964 . Suboptimal Design of Intentionally Non-linear Controllers . IEEE Transactions on Automatic Control , 9 : 380 – 386 .
   Google Scholar
• Sandor , J and Williamson , D . 1977a . Design of Non-linear Regulators for Linear Plants . IEEE Transactions on Automatic Control , 22 : 47 – 50 .
   Web of Science ®Google Scholar
• Sandor , J and Williamson , D . 1977b . Nonlinear Feedback to Improve the Transient Response of a Linear Servo . IEEE Transactions on Automatatic Control , 22 : 863 – 864 .
   Google Scholar
• Seron , M , Braslavsky , J and Goodwin , G . 1997 . Fundamental Limitations in Filtering and Control , London : Springer-Verlag .
   Google Scholar
• Sturm , J . 1999 . Using SEDUMI 1.02, a Matlab Toolbox for Optimisation Over Symmetric Cones . Optimization Methods and Software , 11–12 : 625 – 653 .
   Web of Science ®Google Scholar
• Tan , W and Packard , A . 2006 . “ Stability Region Analysis using Sum of Squares Programming ” . In in IEEE ACC 6 Minneapolis
   Google Scholar