Output Feedback Stabilizing Composited Lurie Systems Based on the Comparison Principle

A comparing model is introduced to transfer the problem of output feedback for stabilizing the Lurie composited nonlinear systems into output feedback stabilizing the comparison systems of lower dimensions, by employing differential and Lyapunov stability theory integrally. A stability condition is developed in form of M matrix, the corresponding LMI expression is founded, which leads to an iterative approach to obtain the output feedback gain. An algorithm to obtain the output-feedback gain matrix is developed here based on the LMI technique. The key technique of developing iterative law of the matrix variable existing in QMI is discussed also. The character of the results proposed here is decreasing complexity. Finally, a numerical example is given to illustrate our results and its application.