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

摘要

An 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 (c) 2007 John Wiley & Sons, Ltd.