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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. © 2012 IEEE.

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