Self-triggering in nonlinear systems: A small gain theorem approach

This paper investigates stability of nonlinear control systems under intermittent information. Building on the small-gain theorem, we develop self-triggered control yielding stable closed-loop systems. We take the violation of the small-gain condition to be the triggering event, and develop a sampling policy that precludes this event by executing the control law with up-to-date information. Based on the properties of the external inputs to the plant, the developed sampling policy yields regular stability, asymptotic stability and L
p
-stability. Control loops are modeled as interconnections of hybrid systems, and novel results on L
p
-stability of hybrid systems are presented. Prediction of the triggering event is achieved by employing L
p
-gains over a finite horizon. In addition, L
p
-gains over a finite horizon produce larger intersampling intervals when compared with standard L
p
-gains. Furthermore, a novel approach for calculation of L
p
-gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking control system.