Robust Least Squares Approach for Tracking Control Synthesis of Unstructured Uncertain Bilinear Systems

This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.