H∞ almost disturbance decoupling for MIMO bilinear systems

A nonlinear design is proposed to find a state feedback controller for bilinear systems such that the closed-loop system is internally stable and achieves disturbance attenuation in nonlinear H_∞ sense. Using a set of positive definite constant matrices, we can define a polynomial related to the system. If, except of the origin of system, the polynomial has no real-zero on a given subset of state space, then we can construct a controller, which solves our problem. It is found that the controller structure could be complicated, but is of computational feasibility, and may require optimization technique to search the solution. We consider both SIMO and MIMO cases with illustrated examples.