Stabilization of continuous‐time homogeneous bilinear systems by constant inputs through nonlinear minimization with applications to the static output feedback stabilization problem

Abstract

AbstractAn algorithm to provide constant‐input stabilizing control inputs for multi‐input continuous‐time bilinear systems is proposed in this paper. The algorithm is based on the formal discrete‐time approximation of the system and the unconstrained nonlinear minimization. The key features of the new algorithm are as follows. First, the formal discrete‐time approximation makes the set of stabilizing control inputs star‐shaped centred at the origin, hence the minimization is to be performed only in a neighbourhood of the origin selected by the designer. Second, the algorithm is always capable of finding a solution if one exists, as long as the minimization inside the neighbourhood is successful. Third, by a slight modification, the algorithm permits us to place all the eigenvalues of the system inside a rectangular region in the complex plane, as long as it is feasible. The algorithm is also applicable to the static output feedback stabilization problem of linear time‐invariant systems. Copyright © 2007 John Wiley & Sons, Ltd.