Considered in this paper is the problem of robust stabilization of a family of interval plants by a single fixed compensator. A frequency domain sufficient condition determines the closed-loop stability. In particular if a specially constructed frequency function does not, at any frequency ω ∈ [0, ∞], intersect the box [−1, 1] × [−1, 1] in the complex plane then the entire closed loop family is stable. Also identified is a class of interval plants for which the sufficient condition in fact does become necessary.
Issue Section:Technical Briefs
Root Locations of an Entire Polytope of Polynomial: It Suffices to Check the Edges,”
Mathematics of Control, Signals and Systems, Vol.
A Generalization of Kharitonov’s Theorem: Robust Stability of Interval Plants,”
IEEE Trans. on Auto Contr., Vol.
34, Mar., pp
Shaw, J., and Jayasuriya, S., 1991, “Robust Stability of Interval Plants: A Geometric Approach for Simplification,” submitted for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL.
Fu, M.Y., 1989, “Polytope of Polynomials with Zeros in Prescribed Region: New Criteria and Algorithms,” Robustness in Identification and Control, M. Milanese, R. Tempo, and A. Vicino, eds., Plenum, NY, pp. 125–146.
Tsypkin, Y., and Polyak, B., 1991, “Frequency Domain Criteria for Robust Stability of Polytope of Polynomials,” Proceedings of the International Workshop on Robust Control, CRC Press, San Antonio, TX, Mar., pp. 491–500.
Anagnost, J., Desoer, C., and Minnichelli, R., 1989, “Generalized Nyquist Tests for Robust Stability: Frequency Domain Generalizations of Kharitonov’s Theorem,” Robustness in Identification and Control, M. Milanese, R. Tempo, and A. Vicino, eds., Plenum, NY, pp. 79–96.
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