Simultaneous ℋ∞ stabilization via fixed-order controllers: Equivalence and computation

This paper is concerned with simultaneous ℋ∞ stabilization with a fixed-order constraint on the controllers for multi-input/multi-output (MIMO) plants. By virtue of a new closed-loop stability and ℋ∞ performance characterization, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation. A convergent iterative algorithm is then provided to solve the condition, and a special property of the feasible solutions enables one to further improve the solvability via simple optimization on initial values. In addition, structural constraints on the controller gains or strong stabilizability can be incorporated into the design procedure in a straightforward manner.

[1]  J. Tsitsiklis,et al.  NP-Hardness of Some Linear Control Design Problems , 1997 .

[2]  Simultaneous stabilization with multiple bounded domains of stability in chemical process control , 1995, Proceedings of IECON '95 - 21st Annual Conference on IEEE Industrial Electronics.

[3]  J. Tsitsiklis,et al.  NP-hardness of some linear control design problems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[4]  Tongwen Chen,et al.  Simultaneous stabilization with near-optimal H∞ performance , 2002, IEEE Trans. Autom. Control..

[5]  P. Olivier.  On the relationship between the model order reduction problem and the simultaneous stabilization problem , 1987 .

[6]  Vincent D. Blondel,et al.  Fault tolerant control: a simultaneous stabilization result , 2004, IEEE Transactions on Automatic Control.

[7]  Ian Postlethwaite,et al.  Simultaneous stabilization of MIMO systems via robustly stabilizing a central plant , 2002, IEEE Trans. Autom. Control..

[8]  T. Djaferis.  To Stabilize a k Real Parameter Affine Family of Plants it Suffices to Simultaneously Stabilize 4k Polynomials , 1991, 1991 American Control Conference.

[9]  Theodore E. Djaferis,et al.  To Stabilize a k Real Parameter Affine Family of Plants it Suffices to Simultaneously Stabilize 4 k Polynomials , 1991 .

[10]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[11]  James Lam,et al.  Simultaneous stabilization via static output feedback and state feedback , 1999, IEEE Trans. Autom. Control..

[12]  W. E. Schmitendorf,et al.  Simultaneous stabilization via linear state feedback control , 1989 .

[13]  J. Murray,et al.  Fractional representation, algebraic geometry, and the simultaneous stabilization problem , 1982 .

[14]  M. Rotea,et al.  An alternative to the D-K iteration? , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[15]  E. Emre.  Simultaneous stabilization with fixed closed-loop characteristic polynomial , 1983 .

[16]  S. Tarbouriech,et al.  Rank-one LMI approach to simultaneous stabilization of linear systems , 1999, 1999 European Control Conference (ECC).

[17]  John N. Tsitsiklis,et al.  A survey of computational complexity results in systems and control , 2000, Autom..

[18]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[19]  Vincent D. Blondel,et al.  Simultaneous stabilizability of three linear systems is rationally undecidable , 1993, Math. Control. Signals Syst..

[20]  Simultaneous stabilization of nonlinear systems , 1984 .

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

[22]  Yeng Chai Soh,et al.  Synthesis of simultaneous stabilizing H∞ Controller controller , 2005 .

[23]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.