Design of Sliding Mode Controllers for Bilinear Systems with Time Varying Uncertainties

Sliding mode controllers for the bilinear systems with time varying uncertainties are developed in this paper. The bilinear coefficient matching condition which is similar to the traditional matching condition for linear system is defined for the homogeneous bilinear systems. It can be seen that the bilinear coefficient matching condition is very limited and is not generally applicable to the nonhomogeneous bilinear system. Thus, the sliding coefficient matching condition is also considered for the bilinear systems with time varying uncertainties. Then, the sufficient conditions are provided for the reaching mode of the time varying uncertain bilinear systems to be guaranteed by the designed sliding mode controllers. Moreover, the stability of the uncertain bilinear systems with the sliding mode controller is discussed. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controllers.