New Results on Sampled-Data Feedback Stabilization for Autonomous Nonlinear Systems

Sufficient conditions are established for sampled-data feedback global asymptotic stabilization for nonlinear autonomous systems. One of our main results is an extension of the well known Artstein-Sontag theorem on feedback stabilization concerning affine in the control systems. A second aim of the present work is to provide sufficient conditions for sampled-data feedback asymptotic stabilization for two interconnected nonlinear systems. Lie algebraic sufficient conditions are derived for the case of affine in the control interconnected systems without drift terms.Comment: 16 page

A General Formula for the Stabilization of Event-Based Controlled Systems

International audienceIn this paper, a universal formula is proposed for event-based stabilization of general nonlinear systems affine in the control. The feedback is derived from the original one proposed by Sontag. Under the assumption of the existence of a smooth Control Lyapunov Function, it enables smooth (except at the origin) global asymptotic stabilization of the origin while ensuring that the sampling interval do not contract to zero. Indeed, for any initial condition within any given closed set the minimal sampling interval is proved to be strictly positive. Under homogeneity assumptions the control can be proved to be smooth anywhere and the sampling intervals bounded below for any initial condition

A General Formula for the Stabilization of Event-Based Controlled Systems

International audienceIn this paper, a universal formula is proposed for event-based stabilization of general nonlinear systems affine in the control. The feedback is derived from the original one proposed by Sontag. Under the assumption of the existence of a smooth Control Lyapunov Function, it enables smooth (except at the origin) global asymptotic stabilization of the origin while ensuring that the sampling interval do not contract to zero. Indeed, for any initial condition within any given closed set the minimal sampling interval is proved to be strictly positive. Under homogeneity assumptions the control can be proved to be smooth anywhere and the sampling intervals bounded below for any initial condition