Robust deadbeat pole assignment with gain constraints: an LMI optimization approach

This paper considers a kind of robust pole assignment problem for discrete-time systems. A recently developed a posteriori measure of closed-loop eigenvalue sensitivity suitable for MIMO deadbeat regulator design is minimized during the search of the state feedback gain. The problem is cast into an LMI-based convex optimization task in which constraints on the size of feedback gain can be catered naturally. The proposed pole assignment algorithm can also be used to find the minimum feedback gain with respect to different norms. A numerical example is then employed to illustrate the effectiveness of the method. Copyright © 2000 John Wiley & Sons, Ltd.

[1]  M. M. Fahmy,et al.  Dead-beat control of linear discrete-time systems , 1983 .

[2]  James Lam,et al.  A gradient flow approach to the robust pole-placement problem , 1995 .

[3]  Parameterization of the class of deadbeat controllers via the theory of decoupling , 1988 .

[4]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[5]  N. Nichols,et al.  Robust pole assignment in linear state feedback , 1985 .

[6]  Hidenori Kimura,et al.  Multivariable dead-beat control with robustness , 1988 .

[7]  J. O'Reilly,et al.  Parametric state-feedback control for arbitrary eigenvalue assignment with minimum sensitivity , 1989 .

[8]  B. Leden,et al.  Multivariable dead-beat control , 1977, Autom..

[9]  James Lam,et al.  Robust deadbeat regulation , 1997 .

[10]  Explicit parameterization of state deadbeat controllers , 1992 .

[11]  Shankar P. Bhattacharyya,et al.  Robust and well‐conditioned eigenstructure assignment via sylvester's equation , 1983 .

[12]  M. A. Murtaza.  Railway managers—creative styles , 1997 .

[14]  Katsuhisa Furuta,et al.  State Variable Methods in Automatic Control , 1988 .

[15]  Paul Van Dooren.  Deadbeat control: A special inverse eigenvalue problem , 1984 .

[16]  J. Lam,et al.  Newton's approach to gain-controlled robust pole placement , 1997 .

[17]  Dean K. Frederick,et al.  Feedback Control Problems Using MATLAB and the Control System Toolbox , 1999 .

[18]  Minimum-gain minimum-time deadbeat controllers , 1988 .

[19]  S. Nash,et al.  Approaches to robust pole assignment , 1989 .

[20]  D. Luenberger.  Canonical forms for linear multivariable systems , 1967, IEEE Transactions on Automatic Control.