On strong stabilization and H/sub /spl infin// strong stabilization problems

In this paper new sufficient conditions for the existence of strongly stabilizing controllers and stable H-infinity controllers are derived in a unified manner. These conditions are recast as the solvability conditions of positive real controller synthesis problem and multi-objective control problem, respectively, which can be solved efficiently via existing linear matrix inequality (LMI) programs. In addition, characterizations of such controllers for both of the problems are given based on the solutions obtained.

[1]  Hitay Özbay,et al.  On the strong stabilization and stable Hinfinity-controller design problems for MIMO systems , 2000, Autom..

[2]  D. Bernstein,et al.  LQG control with an H/sup infinity / performance bound: a Riccati equation approach , 1989 .

[3]  Malcolm C. Smith,et al.  On the order of stable compensators , 1986, Autom..

[4]  James Lam,et al.  Brief On simultaneous H∞ control and strong H∞ stabilization , 2000 .

[5]  Dennis S. Bernstein,et al.  H/sub 2/-suboptimal stable stabilization , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[6]  K. Glover,et al.  State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity , 1988 .

[7]  João Yoshiyuki Ishihara,et al.  Doubly coprime factorizations related to any stabilizing controllers in state space , 1999, Autom..

[8]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[9]  A. Saif.  Parametrization of all stable stablizing controllers , 1998 .

[10]  Michael G. Safonov,et al.  Infinity-Norm Optimization with a Stable Controller , 1985, 1985 American Control Conference.

[11]  Yoshito Ohta,et al.  Unit interpolation in H ∞ : bounds of norm and degree of interpolants , 1991 .

[12]  Yunzhi Li,et al.  An algorithm for interpolation with units in H∞, with applications to feedback stabilization , 1989, Autom..

[13]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[14]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[15]  C. Ganesh,et al.  Design of Optimal Control Systems with Stable Feedback , 1986, 1986 American Control Conference.

[16]  Roland E. Best.  Phase-locked loops : design, simulation, and applications , 2003 .

[17]  Wan Kyun Chung,et al.  On the stable 𝒽∞ controller parameterization under sufficient condition , 2001, IEEE Trans. Autom. Control..

[18]  Michael A. Johnson,et al.  LQG stable stabilizing control: some recent results , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[19]  M. G. Safonov,et al.  Synthesis of positive real feedback systems: a simple derivation via Parrott's theorem , 1997, IEEE Trans. Autom. Control..

[20]  Daniel U. Campos-Delgado,et al.  H/sub /spl infin// strong stabilization , 2001 .

[21]  Ian Postlethwaite,et al.  Strong stabilization of MIMO systems via unimodular interpolation in H , 1998 .

[22]  O. Toker,et al.  On the order of simultaneously stabilizing compensators , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[23]  James Lam,et al.  Stable controller synthesis for linear time-invariant systems , 2002 .

[24]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[25]  M. Vidyasagar.  Control System Synthesis : A Factorization Approach , 1988 .

[26]  Y. WILLIAM WANG,et al.  H2-suboptimal stable stabilization , 1994, Autom..

[27]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[28]  C. Abdallah,et al.  Suboptimal Strong Stabilization Using Fixed-Order Dynamic Compensation , 1990, 1990 American Control Conference.

[29]  Ian Postlethwaite,et al.  Strong stabilization of MIMO systems via H ∞ optimization , 1997 .

[30]  Hitay Özbay,et al.  On the synthesis of stable /spl Hscr//sup /spl infin// controllers , 1999 .