Feedback stabilization for one sided Lipschitz nonlinear systems in reciprocal state space: Synthesis and experimental validation

Assem Thabet – Ghazi Bel Haj Frej – Noussaiba Gasmi – Mohamed Boutayeb

   This paper proposes a design of a stabilization control for one-sided Lipschitz (OSL) nonlinear systems in new reciprocal state space (RSS) framework. The main objective is to extend the state derivative feedback stabilization methods for a class of nonlinear systems where the nonlinearity of derivatives state satisfies the OSL properties in RSS. The presented controller is composed of a state derivative feedback approach in order to ensure asymptotic stability in the sense of Lyapunov. The first approach deals with the synthesis of a basic controller by adopting a simple transformation of Linear Matrix Inequality (LMI) to standard algebraic Ricatti equation (ARE). The second is an extension to adaptive version with adjustment parameters. High performances are shown through real-time implementation with a hardware in the loop (HIL) mode using digital signal processing (DSP) device (DSpace DS 1104).

Keywords: reciprocal state space (RSS), state derivative feedback, ons-sided Lipschitz systems, adaptive control, DSpace DS 1104

[full-paper]