Proportional Nonlinear Systems: A Liable Class for Global Exponential State-Feedback Stabilization

We introduce, through an analysis overall restricted, for the sake of simplicity, in two-dimensions, the class of proportional systems, a nice subclass of the ΣΠ-algebraic nonlinear systems that we formerly introduced in another paper as a sort of ‘non-linear paradigm’ linking nonlinear to bilinear systems. Also we define a decomposition, which every ΣΠ-algebraic system undergoes, into the cascade of a driver, medial and final bilinear subsystem, having the same input-output behavior as the original. We show that a systematic way for global feedback stabilization can be developed for the class of proportional systems, leading to the global feedback exponential stabilization of the medial part under some ‘natural’ condition of non singularity. We show in an example the capability of the proposed method to achieving global feedback stabilization for the original system as well.