State and output feedback control for Lipschitz nonlinear systems in reciprocal state space: synthesis and real-time validation

Assem Thabet (University of Gabes)
Ghazi Bel Haj Frej (University of Bordeaux)
Noussaiba Gasmi (ECAM Rennes-Louis de Broglie)
Karim Mansouri (Université de Nantes-France)
Eric Chauveau (Université de Nantes-France)

Bulletin of Electrical Engineering and Informatics
Vol 11, No 5: October 2022

In industrials process and many studies cases, state and output derivative variables can be easily modeled in reciprocal state space (RSS) form than the standard one. Formulation of stabilization problem with a guaranteed cost control using feedback principle for Lipschitz nonlinear systems (LNS) in RSS is presented in this brief. The asymptotic stability, using the proper Lyapunov functions of the closed-loop system, is guaranteed. The control design problem is guaranteed through a resolution of linear matrix inequalities (LMI) technique under certain lemmas and minimization of non-standard cost control. Experimental validation shows the good performances of the proposed method using real-time implementation (RTI) with a digital signal processing (DSP) device (Arduino MEGA 2560).