Brief Paper: Asynchronous networked control of linear systems via L2-gain-based transformations: analysis and synthesis

This study presents a method to analyse the stability of the feedback interconnection of a class of systems, when the signals associated with the feedback interconnection are sampled asynchronously. A transformation based on L₂-gain is designed and introduced on both sides of the interconnection. This transformation enlarges the maximum sampling time such that the interconnection remains stable. The transformation is designed in such a way that both systems have finite L₂-gain and verifies the small-gain theorem. This design method makes easier the migration of wired continuous-time control loops to unwired asynchronous ones by just adding this transformation to both sides of the interconnection. The analysis is performed by using the concept of maximum sampling time that preserves small gain (MASG), starting from the continuous-time definition of the property. Finally, a synthesis method is included to obtain the transformation, assuming that the minimum sampling time available in the communication channel is given as a constraint. The synthesis method follows an iterative procedure and solves a set of matrix inequalities. We report on real experiments applied to the remote control of the rotor speeds of a quadrotor.