Co-design of output feedback laws and event-triggering conditions for the L-2-stabilization of linear systems

We investigate the
L2
-stabilization of linear systems using output feedback event-triggered controllers. In particular, we are interested in the scenario where the plant output and the control input are transmitted to the controller and to the actuators, respectively, over two different digital channels, which have their own sampling rule. The plant dynamics is affected by external disturbances and the output measurement and the control input are corrupted by noises. We present a co-design procedure to simultaneously synthesize dynamic output feedback laws and event-triggering conditions such that the closed-loop system is L2-stable with a given upper-bound on the
L2-gain. The required conditions are formulated in terms of the feasibility of linear matrix inequalities (LMIs). Then, we exploit these LMIs to maximize the guaranteed minimum time between two transmissions of the plant output and/or of the control input. We also present a heuristic method to reduce the amount of transmissions for each channel. The developed technique encompasses time-driven (and so periodic) sampling as a particular case and the result is also new in this context. The effectiveness of the proposed methods is illustrated on a numerical example.