Paper: Characterization of equilibrium sets for bilinear systems with feedback control

Authors:
A. Benallou;D. A. Mellichamp;D. E. Seborg
Affiliations:
Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, U.S.A.;Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, U.S.A.;Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, U.S.A.
Venue:
Automatica (Journal of IFAC)
Year:
1983

Citing 3
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Abstract

Simple analytical methods for the characterization of the equilibrium sets of bilinear systems with linear feedback control are developed based on elimination theory. It is shown that the number of equilibrium points can be determined as a function of the feedback gains, without having to solve for the locations of the equilibrium points. Necessary and sufficient conditions for the origin to be the unique equilibrium point are also presented. These results provide the basis for computing the equilibrium points via a straightforward procedure, which eliminates the convergence, stability and uncertainty problems that can occur when iterative root finding techniques are used. Several illustrative examples are included. The methods developed in this paper can also be used to characterize the equilibrium sets of other classes of nonlinear systems such as quadratic systems.