A Multiplier Approach for the Robust Design of Discrete-Time Control Systems with Real/Complex Uncertainties

A novel approach for the design of robust controllers for discrete-time uncertain systems using a multiplier approach is given. Our algorithm is based on a k"m/@m-synthesis type iteration involving a search for suitable multipliers and solving scaled H"~ optimization problems. The latter problems involve only the original plant data and the scalings are computed via standard spectral factorizations from the multiplier. The design is performed entirely in the discrete-time domain and the results can be used for multiobjective control design (Tchernychev and Sideris, 1997).

[1]  K. Glover,et al.  State-space approach to discrete-time H∞ control , 1991 .

[3]  Hector Rotstein,et al.  Discrete-time H, Control: The One-Block Case , 1992 .

[4]  M. Athans,et al.  A multiloop generalization of the circle criterion for stability margin analysis , 1981 .

[5]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[6]  M. Safonov,et al.  Real/complex multivariable stability margin computation via generalized Popov multiplier-LMI approach , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[7]  A. Tits,et al.  Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics , 1991 .

[8]  k/sub m/-design with time domain constraints , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[9]  D. Bernstein,et al.  Extensions of mixed- mu bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. I , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[10]  M. Safonov,et al.  Real/Complex Km-Synthesis without Curve Fitting , 1993 .

[11]  Brian D. O. Anderson,et al.  Recursive algorithm for spectral factorization , 1974 .

[12]  P. Young.  Controller design with real parametric uncertainty , 1996 .

[13]  A. Packard,et al.  Linear matrix inequalities in analysis with multipliers , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  John Doyle,et al.  Structured uncertainty in control system design , 1985, 1985 24th IEEE Conference on Decision and Control.