H_∞ ALMOST DISTURBANCE DECOUPLING FOR MIMO BILINEAR SYSTEMS

The H_∞ almost disturbance decoupling problem is considered. In this paper, a nonlinear design is proposed to find a state feedback controller for bilinear systems. The closed-loop system is internally stable and achieves disturbance attenuation in nonlinear H_∞ sense. We defined a special form of Lyapunov function, which is constructed in terms of one or a set of positive definite constant matrices. If, except of the origin of system, the corresponding polynomial of the positive definite matrix (or several polynomials relevant to the positive definite constant matrices) has (have) no zero on a given subset of state space, then we can construct a controller to solve our problem. It is found that the controller structure could be complicated, but is feasible in computation and may require optimization technique to search the solution. We consider both SIMO and MIMO cases with illustrated examples.