H_∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation

References

• Anderson , BDO and Liu , Y . 1989 . Controller Reduction: Concepts and Approaches . IEEE Transactions on Automatic Control , 34 : 802 – 812 .
   Web of Science ®Google Scholar
• Bertsekas , DP . 1995 . Nonlinear Programming , Belmont, Mass : Athena Scientific .
   Google Scholar
• Blondel , V and Tsitsiklis , JN . 1997 . NP-hardness of Some Linear Control Design Problems . SIAM Journal of Control Optimization , 35 ( 6 ) : 2118 – 2127 .
   Web of Science ®Google Scholar
• Boyd , S , Ghaoui , LE , Feron , E and Balakrishnan , V . 1994 . Linear Matrix Inequalities in System and Control Theory , Philadelphia, PA : SIAM Studies in Applied Mathematics .
   Google Scholar
• Chilali , M and Gahinet , P . 1996 . H ∞ Design with Pole Placement Constraints: An LMI Approach . IEEE Transactions on Automatic Control , 41 ( 3 ) : 358 – 367 .
   Web of Science ®Google Scholar
• Costa , OLV and Fragoso , MD . 1993 . Stability Results for Discrete-time Linear Systems with Markovian Jumping Parameters . Journal of Mathematical Analysis and Applications , 179 ( 1 ) : 154 – 178 .
   Web of Science ®Google Scholar
• Ebihara , Y and Hagiwara , T . 2004 . On H ∞ Model Reduction Using LMIs . IEEE Transactions on Automatic Control , 49 ( 7 ) : 1187 – 1191 .
   Google Scholar
• Gahinet , P , Nemirovski , A , Laub , AJ and Chilali , M . 1995 . LMI Control Toolbox for Use with Matlab , Natick, MA : The MathWorks Parter Series .
   Google Scholar
• Ghaoui , LE and Rami , MA . 1996 . Robust State-feedback Stabilisation of Jump Linear Systems via LMIS . International Journal of Robust Nonlinear Control , 6 : 1015 – 1022 .
   Web of Science ®Google Scholar
• Ghaoui , LE , Oustry , F and Rami , MA . 1997 . A Cone Complementarity Linearisation Algorithm for Static Output-feedback and Related Problems . IEEE Transactions on Automatic Control , 42 ( 8 ) : 1171 – 1176 .
   Web of Science ®Google Scholar
• Glover , K . 1984 . All Optimal Hankel Norm Approximation of Linear Multivariable Systems and Their L ∞-error Bounds . International Journal of Control , 39 ( 6 ) : 1115 – 1193 .
   Web of Science ®Google Scholar
• Grigoriadis , KM . 1995 . Optimal H ∞ Model Reduction via Linear Matrix Inequalities . Systems & Control Letters , 26 ( 5 ) : 321 – 333 .
   Web of Science ®Google Scholar
• Kavranoglu , D . 1994 . A Computational Scheme for H ∞ Model Reduction . IEEE Transactions on Automatic Control , 39 ( 7 ) : 1447 – 1451 .
   Google Scholar
• Lee , KH , Lee , JH and Kwon , WH . 2004 . A Non-linear Minimisation Approach to Multiobjective and Structured Controls for Discrete-time Systems . International Journal of Robust Nonlinear Control , 14 ( 16 ) : 1327 – 1343 .
   Google Scholar
• Li , L and Paganini , F . 2005 . Structured Coprime Factor Model Reduction Based on LMIs . Automatica , 41 ( 1 ) : 145 – 151 .
   Google Scholar
• Meyer , DG . 1990 . Fractional Balanced Reduction: Model Reduction via Fractional Representation . IEEE Transactions on Automatic Control , 35 : 1341 – 1345 .
   Web of Science ®Google Scholar
• Moore , B . 1981 . Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction . IEEE Transactions on Automatic Control , 26 : 17 – 31 .
   Web of Science ®Google Scholar
• Rami , MA and Ghaoui , LE . H ∞ State-feedback of Jump Linear Systems . Proceedings of the 34th IEEE Conference on Decision and Control . 1995 . pp. 951 – 952 . New Orleans, LA
   Google Scholar
• Seiler , P and Sengupta , R . 2003 . A Bounded Real Lemma for Jump Systems . IEEE Transactions on Automatic Control , 48 ( 9 ) : 1651 – 1654 .
   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 .
   Web of Science ®Google Scholar
• Vandenberghe , L and Boyd , S . 1996 . Semidefinite Programming . SIAM Review , 38 ( 1 ) : 49 – 95 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J , Huang , S and Yang , C . 2001 . H ∞ Model Reduction for Linear Time-delay Systems: Continuous-time Case . International Journal of Control , 74 ( 1 ) : 1062 – 1074 .
   Google Scholar
• Zhang , L , Huang , B and Lam , J . 2003 . H ∞ Model Reduction of Markovian Jump Linear Systems . Systems & Control Letters , 50 : 103 – 118 .
   Web of Science ®Google Scholar