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.
- Dynamic Systems and Control Division
Proportional Nonlinear Systems: A Liable Class for Global Exponential State-Feedback Stabilization
Carravetta, F. "Proportional Nonlinear Systems: A Liable Class for Global Exponential State-Feedback Stabilization." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control. Palo Alto, California, USA. October 21–23, 2013. V003T34A003. ASME. https://doi.org/10.1115/DSCC2013-3761
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