Transition processes in the SISO system incorporating an observer in the control loop are discussed. The symmetry of the transition matrix with respect to the eigenvalues assigned for the controller and the observer is proved using state space methods. The interrelation with the peaking phenomenon is discussed, asymptotic behavior of the system with a fast observer is analyzed, and illustrative examples are presented. [S0022-0434(00)02102-X]
Issue Section:
Technical Papers
1.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley, New York.
2.
Polotsky
, V.
, 1980
, “Estimation of the state of single-output linear systems by means of observers
,” Autom. Remote Control (Engl. Transl.)
, 12
, pp. 1640
–1648
.3.
Kimura
, H.
, 1981
, “A New Approach to the Perfect Regulation and the Bounded Peaking in Linear Multivariable Systems
,” IEEE Trans. Autom. Control.
, AC-26
, pp. 253
–270
.4.
Sussmann
, H. J.
, and Kokotovic
, P.
, 1991
, “The Peaking Phenomenon and the Global Stabilization of Nonlinear Systems
,” IEEE Trans. Autom. Control.
, AC-36
, pp. 424
–440
.5.
Sada
, N.
, and Fujii
, T.
, 1981
, “The Optimality Property of an Optimal Regulator Incorporating an Observer
,” Int. J. Control
, 33
, pp. 617
–647
.6.
Andry
, A. N.
, Chung
, J. C.
, and Shapiro
, E. T.
, 1984
, “Modalized Observers
,” IEEE Trans. Autom. Control.
, AC-29
, pp. 669
–672
.7.
Jabberi
, F.
, and Shmitendorf
, W.
, 1991
, “Robust Linear Controllers Using Observers.
” IEEE Trans. Autom. Control.
, AC-36
, pp. 1509
–1514
.8.
Esfandari
, F.
, and Khalil
, H. K.
, 1992
, “Output Feedback Stabilization of Fully Linearizable Systems
,” Int. J. Control
, 56
, pp. 1007
–1037
.9.
Friedland
, B.
, Meutzlopoulou
, S.
, and Antoniou
, G.
, 1993
, “On a Property of Compensators Designed by the Separation Principle
,” IEEE Trans. Autom. Control.
, AC-38
, pp. 370
–373
.10.
Bender
, D. J.
, 1985
, “Some Consideration for Estimator-Based Compensator Design
,” Int. J. Control
, 41
, pp. 1577
–1588
.11.
Fowel
, D. J.
, and Benderand
, R. A.
, 1985
, “Computing the Estimator-Controller Form of a Compensator
,” Int. J. Control
, 41
, pp. 1565
–1576
.12.
Polotski, V., 1997, “The Response of the System Incorporating an Observer in the Control Loop,” ACC97, New Mexico, pp. 3465–3469.
13.
Polotsky
, V.
, 1978
, “On the Maximal Errors of an Asymptotic State Identifier
,” Autom. Remote Control (Engl. Transl.)
, 8
, pp. 1116
–1121
.14.
Atassi
, A. N.
, and Khalil
, H. K.
, 1999
, “A Separation Principle for the Stabilization of a Class of Nonlinear Systems
,” IEEE Trans. Autom. Control.
, AC-44
, pp. 1672
–1687
.15.
Gantmacher, F. R., 1969, The Theory of Matrices, Chelsea, New York.
16.
Kokotovic, P. V., and Khalil, H. K., 1986, Singular Perturbation in Systems and Control, IEEE Press, New York.
Copyright © 2000
by ASME
You do not currently have access to this content.