Output feedback control for bilinear system using Legendre polynomials

In this paper, we propose a new approach to design output feedback regulators for bilinear system by the mean of shifted Legendre polynomials. The proposed technique is based on the projection of the controlled system and the linear reference model that it should follow. The useful properties of the considered basis such as operational matrices combined with the Kronecker product transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. Simulation result is included to demonstrate the validity and applicability of the technique.