Real Time Stabilization of Lipschitz Nonlinear Systems with Nonlinear Output

Abstract

This brief discusses a simple stabilization strategy for a class of Lipschitz nonlinear systems based on the transformation of nonlinear function to Linear Parameter Varying system. Due to the introduction of the Differential Mean Value Theorem (DMVT), the dynamic and output nonlinear functions are transformed into Linear Parameter Varying (LPV) functions. This allows to increase the number of decision variables in the constraint to be resolved and, then, get less conservative and more general Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of LMI with the introduction of a cost control to ensure closed-loop stability. Finally, Real Time Implementation (RTI) using a DSP device (ARDUINO UNO R3) to a typical robot is given to illustrate the performances of the proposed method with a comparison to some existing results.