Robust model-reference control for a class of non-linear and piece-wise linear systems

This paper demonstrates a strategy for designing model-reference controllers. The design technique is based on using Backstepping techniques as an extension to Lyapunov-based designs. The proposed controller has the capability of accomplishing both asymptotic stability and satisfactory transient performance. LMI techniques are used to investigate the stability of the proposed controller when the model could be expressed in an affine-based form. Two different approaches are used to deal with nonlinear systems. The first one is by using different affine models for the system with a scheduling parameter to switch between the models. The second one is by directly using the nonlinear system while adding pole-placement structure to the closed loop system. Full state feedback, output feedback and robustness problems are addressed in the existence of uncertainties. A simulated one-degree of freedom robot arm, in a MATLAB/SIMULINK environment, is used to exemplify the suggested techniques along with the LMI toolbox. Tradeoffs between stability and performance are carefully studied