Stabilizing controllers for bilinear systems

Abstract

The problem of finding stabilizing feedback controllers for continuous bilinear systems, where the controls act additively and multiplicatively simultaneously, is treated. The applicability of the "quadratic" control law of Jacobson [5] and others is extended to the case when the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> -matrix has arbitary, eigenvalues under certain conditions. A class of bilinear systems common among biochemical flow systems is defined: the dyadic bilinear systems. A control scheme, the so-called division controller, for dyadic bilinear systems is suggested. The practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor.