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If the system is such that (26) cannot be satisfied, then, as shown by Madiwale and
Williams, an condition analogous to the full order Doyle-Stein condition can be derived
from (29) in the case of a scalar control input. The condition is ( ⎡I − K I + A Φ K
⎣ ) −1 where ( Φ 22 = s I − A 22 ) ( ) A 12Φ22 ⎤ B 2 − KB1 = 0
⎦ −1 ©Encyclopedia of Life Support Systems (EOLSS) (33) CONTROL SYSTEMS, ROBOTICS AND AUTOMATION - Vol. VIII - Reduced-Order State Observers - Bernard Friedland - TO ACCESS ALL THE 11 PAGES OF THIS CHAPTER,
S A.N. Madiwale and D.E. Williams (1985) “Some Extensions of Loop Transfer Recovery”, Proceedings,
American Control Conf., Boston, MA, pp. 790-795. [Provides generalization of Doyle-Stein robustness
condition for reduced-order observers.]
B. Friedland (1986) Control System Design: An Introduction to State-Space Methods, McGraw-Hill Book
Co., New York. [Textbook on linear control theory including full-order and reduced-order observers and
B. Friedland (1989) “On the properties of Reduced-Order Kalman Filters” IEEE Trans. on Automatic
Control, Vol.34, No.3, pp.321-324 [Results for theory of linear, reduced-order observers.]
D. Luenberger (1966) “Observers for Multivariable Systems”, IEEE Trans. on Automatic Control, Vol.
AC-11, pp.190-197. [Exposition of the general theory of linear observers, including reduced-order
E.G. Rynaski (1982) “Flight Control Synthesis Using Robust Observers”, Proceedings, AIAA Guidance
and Control Conf., San Diego, CA, pp. 825-831. [Introduces theory of robust observer and its role in
linear control system design.] J.C. Doyle and G. Stein (1979) “Robustness with Observers,” IEEE Trans. on Automatic Control, Vol.
AC-24, pp. 607-611.[Discusses robustness problems of observer-based linear control system design.] R.W. Bass and I. Gura (1965) “High-Order System Design Via State-Space Considerations”, Proc. Joint
Automatic Control Conf., Troy, NY, pp.311-318. [Many interesting results for linear control systems,
including formula for pole-placement.]
W.S. Levine, ed. (1996) The Control Handbook CRC Press and IEEE Press. [Contains a number of
articles on observers and Kalman filters.]
Biographical Sketch Bernard Friedland is a Distinguished Professor in the Department of Electrical and Computer
Engineering at the New Jer...
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- Spring '14