Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations

References

• Apkarian , P and Adams , RJ . 1998 . Advanced Gain-scheduling Techniques for Uncertain Systems . IEEE Transactions on Control Systems Technology , 6 : 21 – 32 .
   Web of Science ®Google Scholar
• Apkarian , P and Gahinet , P . 1995 . A Convex Characterization of Gain-scheduled ℋ∞ Controllers . IEEE Transactions on Automatic Control , 40 : 853 – 864 .
   Web of Science ®Google Scholar
• Bernussou , J , Peres , PLD and Geromel , JC . 1989 . A Linear Programming Oriented Procedure for Quadratic Stabilization of Uncertain Systems . Systems & Control Letters , 13 : 65 – 72 .
   Web of Science ®Google Scholar
• Bliman , P-A . 2004 . An Existence Result for Polynomial Solutions of Parameter-dependent LMIs . Systems & Control Letters , 51 : 165 – 169 .
   Web of Science ®Google Scholar
• Bliman , P-A . 2005 . “ ‘Stabilization of LPV systems’ ” . In Positive Polynomials in Control, Volume 312 of Lecture Notes in Control and Information Sciences , Edited by: Henrion , D and Garulli , A . 103 – 117 . Berlin : Springer Verlag .
   Google Scholar
• Bliman , P-A , Oliveira , RCLF , Montagner , VF and Peres , PLD . 2006 . “ Existence of Homogeneous Polynomial Solutions for Parameter-dependent Linear Matix Inequalities with Parameters in the Simplex ” . In in Proceedings of the 45th IEEE Conference on Decision and Control 1486 – 1491 . San Diego, CA
   Google Scholar
• Boyd , S , El Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . “ Linear Matrix Inequalities in System and Control Theory ” . In SIAM Studies in Applied Mathematics , Philadelphia, PA : SIAM .
   Google Scholar
• Boyd , S and Vandenberghe , L . 2004 . Convex Optimization , Cambridge, , UK : Cambridge University Press .
   Google Scholar
• Chesi , G , Garulli , A , Tesi , A and Vicino , A . 2004a . “ Parameter-dependent Homogeneous Lyapunov Functions for Robust Stability of Linear Time-varying Systems ” . In in Proceedings of the 43rd IEEE Conference on Decision and Control 4095 – 4100 . Paradise Island, Bahamas
   Google Scholar
• Chesi , G , Garulli , A , Tesi , A and Vicino , A . 2004b . Robust Analysis of LFR Systems Through Homogeneous Polynomial Lyapunov Functions . IEEE Transactions on Automatic Control , 49 : 1211 – 1216 .
   Web of Science ®Google Scholar
• Chesi , G , Garulli , A , Tesi , A and Vicino , A . 2005 . Polynomially Parameter-dependent Lyapunov Functions for Robust Stability of Polytopic Systems: An LMI Approach . IEEE Transactions on Automatic Control , 50 : 365 – 370 .
   Web of Science ®Google Scholar
• Chesi , G , Garulli , A , Tesi , A and Vicino , A . 2007 . Robust Stability of Time-varying Polytopic Systems via Parameter-dependent Homogeneous Lyapunov Functions . Automatica , 43 : 309 – 316 .
   Web of Science ®Google Scholar
• de Oliveira , MC and Skelton , RE . 2001 . “ Stability Tests for Constrained Linear Systems ” . In Perspectives in Robust Control, Volume 268 of Lecture Notes in Control and Information Science , Edited by: Reza Moheimani , SO . Vol. 268 , 241 – 257 . New York : Springer-Verlag .
   Google Scholar
• de Souza , CE and Trofino , A . 2006 . Gain-scheduled ℋ2 Controller Synthesis for Linear Parameter Varying Systems via Parameter-dependent Lyapunov Functions . International Journal of Robust and Nonlinear Control , 16 : 243 – 257 .
   Web of Science ®Google Scholar
• Gahinet , P , Apkarian , P and Chilali , M . 1996 . Affine Parameter-dependent Lyapunov Functions and Real Parametric Uncertainty . IEEE Transactions on Automatic Control , 41 : 436 – 442 .
   Web of Science ®Google Scholar
• Gahinet , P , Nemirovskii , A , Laub , AJ and Chilali , M . 1995 . LMI Control Toolbox User's Guide Natick, MA The Math Works Inc
   Google Scholar
• Gao , H , Meng , X and Chen , T . 2008 . A New Design of Robust H2 Filters for Uncertain Systems . Systems & Control Letters , 57 : 585 – 593 .
   Web of Science ®Google Scholar
• Geromel , JC and Colaneri , P . 2006 . Robust Stability of Time Varying Polytopic Systems . Systems & Control Letters , 55 : 81 – 85 .
   Web of Science ®Google Scholar
• Geromel , JC , de Oliveira , MC and Hsu , L . 1998 . LMI Characterization of Structural and Robust Stability . Linear Algebra and its Applications , 285 : 69 – 80 .
   Web of Science ®Google Scholar
• Geromel , JC and Korogui , RH . 2006 . “ Matrix Quadratic Polynomials with Application to Robust Stability Analysis ” . In in Proceedings of the 5th IFAC Symposium on Robust Control Design (ROCOND 2006) Toulouse, France
   Google Scholar
• Henrion , D and Garulli , A . 2005 . Positive Polynomials in Control, Volume 312 of Lecture Notes on Control and Information Sciences , Berlin : Springer-Verlag .
   Google Scholar
• Henrion , D and Lasserre , JB . 2006 . Convergent Relaxations of Polynomial Matrix Inequalities and Static Output Feedback . IEEE Transactions on Automatic Control , 51 : 192 – 202 .
   Web of Science ®Google Scholar
• Iwasaki , T . 1996 . Robust Performance Analysis for Systems with Structured Uncertainty . International Journal of Robust and Nonlinear Control , 6 : 85 – 99 .
   Web of Science ®Google Scholar
• Khalil , HK . 1996 . Nonlinear Systems , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Köroğlu , H and Scherer , CW . 2007 . Robust Performance Analysis for Structured Linear Time-varying Perturbations with Bounded Rates-of-variation . IEEE Transactions on Automatic Control , 52 : 197 – 211 .
   Google Scholar
• Leite , VJS and Peres , PLD . 2003 . An Improved LMI Condition for Robust 𝒟-stability of Uncertain Polytopic Systems . IEEE Transactions on Automatic Control , 48 : 500 – 504 .
   Web of Science ®Google Scholar
• Leith , DJ and Leithead , WE . 2000 . Survey of Gain-scheduling Analysis and Design . International Journal of Control , 73 : 1001 – 1025 .
   Web of Science ®Google Scholar
• Lin , C , Wang , Q-G and Lee , TH . 2006 . Less Conservative 𝒟-stability Test for Polytopic Systems using Linearly Parameter-dependent Lyapunov Functions . IEE Proceedings–Control Theory and Applications , 153 : 665 – 670 .
   Google Scholar
• Löfberg , J . 2004 . “ YALMIP: A Toolbox for Modelling and Optimisation in MATLAB ” . In in Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design 284 – 289 . Taipei, Taiwan http://control.ee.ethz.ch/~joloef/yalmip.php
   Google Scholar
• Montagner , VF , Leite , VJS and Peres , PLD . 2003 . “ Robust Control of Discrete Time Switched Systems with Pole Location and Structural Constraints ” . In in Proceedings of the 42nd IEEE Conference on Decision and Control 6242 – 6247 . Maui, HI, , USA
   Google Scholar
• Montagner , VF , Oliveira , RCLF and Peres , PLD . 2006 . “ Design of ℋ∞ Gain-scheduled Controllers for Linear Time-varying Systems by Means of Polynomial Lyapunov Functions ” . In in Proceedings of the 45th IEEE Conference on Decision and Control 5839 – 5844 . San Diego, CA, , USA
   Google Scholar
• Montagner , VF and Peres , PLD . 2004 . Robust Stability and ℋ∞ Performance of Linear Time-varying Systems in Polytopic Domains . International Journal of Control , 77 : 1343 – 1352 .
   Web of Science ®Google Scholar
• Montagner , VF and Peres , PLD . 2006 . State Feedback Gain Scheduling for Linear Systems with Time-varying Parameters . Journal of Dynamic Systems, Measurement and Control–Transactions of ASME , 128 : 365 – 370 .
   Google Scholar
• Oliveira , RCLF and Peres , PLD . 2005 . Stability of Polytopes of Matrices via Affine Parameter-dependent Lyapunov Functions: Asymptotically Exact LMI Conditions . Linear Algebra and its Applications , 405 : 209 – 228 .
   Web of Science ®Google Scholar
• Oliveira , RCLF and Peres , PLD . 2006 . LMI Conditions for Robust Stability Analysis Based on Polynomially Parameter-dependent Lyapunov Functions . Systems & Control Letters , 55 : 52 – 61 .
   Web of Science ®Google Scholar
• Oliveira , RCLF and Peres , PLD . 2007 . Parameter-dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-dependent Solutions via LMI Relaxations . IEEE Transactions on Automatic Control , 52 : 1334 – 1340 .
   Web of Science ®Google Scholar
• Parrilo , PA . 2003 . Semidefinite Programming Relaxations for Semialgebraic Problems . Mathematical Programming: Series B , 96 : 293 – 320 .
   Web of Science ®Google Scholar
• Peaucelle , D , Arzelier , D , Bachelier , O and Bernussou , J . 2000 . A New Robust 𝒟-stability Condition for Real Convex Polytopic Uncertainty . Systems & Control Letters , 40 : 21 – 30 .
   Web of Science ®Google Scholar
• Ramos , DCW and Peres , PLD . 2002 . An LMI Condition for the Robust Stability of Uncertain Continuous-time Linear Systems . IEEE Transactions on Automatic Control , 47 : 675 – 678 .
   Web of Science ®Google Scholar
• Rugh , WJ and Shamma , JS . 2000 . Research on Gain Scheduling . Automatica , 36 : 1401 – 1425 .
   Web of Science ®Google Scholar
• Scherer , CW . 2003 . “ Higher-order Relaxations for Robust LMI Problems with Verifications for Exactness ” . In in Proceedings of the 42nd IEEE Conference on Decision and Control 4652 – 4657 . Maui, HI, , USA
   Google Scholar
• Scherer , CW . 2005 . Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness . SIAM Journal on Matrix Analysis and Applications , 27 : 365 – 395 .
   Web of Science ®Google Scholar
• Scherer , CW and Hol , CWJ . 2006 . Matrix Sum-of-squares Relaxations for Robust Semi-definite Programs . Mathematical Programming: Series B , 107 : 189 – 211 .
   Web of Science ®Google Scholar
• Scorletti , G and El Ghaoui , L . 1998 . Improved LMI Conditions for Gain Scheduling and Related Control Problems . International Journal of Robust and Nonlinear Control , 8 : 845 – 877 .
   Web of Science ®Google Scholar
• Shamma , JS and Athans , M . 1991 . Guaranteed Properties of Gain Scheduled Control for Linear Parameter-varying Plants . Automatica , 27 : 559 – 564 .
   Web of Science ®Google Scholar
• Skelton , RE , Iwasaki , T and Grigoriadis , K . 1998 . A Unified Algebraic Approach to Linear Control Design , Bristol, PA : Taylor & Francis .
   Google Scholar
• Stilwell , DJ and Rugh , WJ . 1999 . Interpolation of Observer State Feedback Controllers for Gain Scheduling . IEEE Transactions on Automatic Control , 44 : 1225 – 1229 .
   Web of Science ®Google Scholar
• Sturm , JF . 1999 . Using SeDuMi 1.02, A MATLAB Toolbox for Optimization Over Symmetric Cones . Optimization Methods and Software , 11–12 : 625 – 653 . http://sedumi.mcmaster.ca/
   Web of Science ®Google Scholar
• Trofino , A and de Souza , CE . 2001 . Biquadratic Stability of Uncertain Linear Systems . IEEE Transactions on Automatic Control , 46 : 1303 – 1307 .
   Google Scholar
• Wang , F and Balakrishnan , V . 2002 . Improved Stability Analysis and Gain-scheduled Controller Synthesis for Parameter-dependent Systems . IEEE Transactions on Automatic Control , 47 : 720 – 734 .
   Web of Science ®Google Scholar
• Wu , F . 2001 . A Generalized LPV System Analysis and Control Synthesis Framework . International Journal of Control , 74 : 745 – 759 .
   Web of Science ®Google Scholar