Mean Square Exponential Stabilization of Sampled-Data Systems Subject to Actuator Nonlinearities, Random Sampling, and Packet Dropouts

This work deals with the mean square exponential stabilization of sampled-data linear systems subject to sector-bounded actuator nonlinearities and to aperiodic sampling intervals, which are assumed to be Erlang-distributed random variables. The possibility of packet dropouts is also taken into account and modeled by a Bernoulli process. Linear matrix inequality (LMI) conditions are proposed to design a stabilizing state-feedback controller for the system. Moreover, it is shown that the method leads to necessary and sufficient stabilization conditions in the absence of actuator nonlinearities. The results are derived using the framework of piecewise deterministic Markov processes, a subclass of stochastic hybrid systems.