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Disturbance rejection by proportional and derivative output feedback. (English) Zbl 0859.93022
The paper deals with the disturbance rejection of linear systems of the form $$\dot x=Ax+Bu$$, $$y=Cx+e$$ where $$e$$ is a disturbance signal. As a solution, the authors propose a nonproper solution containing proportional and derivative (state) feedback. To avoid the nonproperness of the given solution, an approximate proper control scheme is given. Such approximate solutions are discussed for both minimum phase and non-minimum phase systems, and are illustrated by means of a few simulation examples.

##### MSC:
 93B52 Feedback control 93C73 Perturbations in control/observation systems 93B27 Geometric methods
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##### References:
 [1] M. Bonilla, M. Malabre: Solvability and one side invertibility for implicit Descriptions. 29th IEEE-CDC, Vol. 6, pp. 3601-3602, Honolulu, Hawaii 1990. [2] M. Bonilla, M. Malabre: Redundant and non observable spaces of implicit descriptions. 30th IEEE-CDC, Vol. 2, pp. 1425-1430, Brighton, U.K. 1991. [3] M. Bonilla M. Fonseca, M. Malabre: Implementing non proper control laws for proper systems. International Symposium of Implicit and Nonlinear Systems, SINS’92 (F. Lewis, Automation and Robotics Research Institute), Ft. Worth Texas, U.S.A. 1992, pp. 163-169. [4] M. Bonilla, M. Malabre: External reachability (reachability with pole assignment by P. D. feedback) for implicit descriptions. Kybernetika 29 (1993), 5, 499-510. · Zbl 0802.93025 · www.kybernetika.cz · eudml:27690 [5] M. Bonilla, M. Malabre: Geometric characterizations of external minimality for implicit descriptions. Proceedings of the 32nd IEEE-CDC, Vol. 4, San Antonio, Texas 1993, pp. 3311-3312. [6] M. Bonilla, M. Malabre: Convergence in behavior to non proper systems. Proceedings of the 33rd IEEE-CDC, Vol. 2, pp. 1002-1003, Vol 4., Orlando, Florida 1994. [7] F. R. Gantmacher: The Theory of Matrices. Part 2. Chelsea Publishing Co., N.Y. 1959. · Zbl 0085.01001 [8] J. Grimm: Application de la Theorie des Systemes Implicites a l’inversion des Systemes. Proc. 6th International Conference on Analysis and Optimization of Systems. Lecture Notes in Control and Inform. Sci. 63 (1984), 142-156. · Zbl 0556.93026 [9] G. Lebret, J. J. Loiseau: Proportional and proportional derivative canonical forms for descriptor systems with outputs. Automatica 30 (1994), 5, 847-864. · Zbl 0814.93021 · doi:10.1016/0005-1098(94)90173-2 [10] F. L. Lewis: A Tutorial on the geometric analysis of linear time-invariant implicit systems. Automatica 28 (1992), 1, 119-137. · Zbl 0745.93033 · doi:10.1016/0005-1098(92)90012-5 [11] A. S. Morse: Structural invariants of linear multivariable systems. SIAM J. Control Optim. 11 (1973), 3, 446-465. · Zbl 0259.93011 · doi:10.1137/0311037 [12] W. M. Wonham: Linear Multivariable Control: A Geometric Approach. Fifth edition. Springer-Verlag, New York 1985. · Zbl 0609.93001
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