Output-Feedback Stabilization of Stochastically-Sampled Networked Control Systems Under Packet Dropouts

This paper deals with the mean-square output feedback stabilization of sampled-data linear time-invariant (LTI) systems in the presence of sporadically sampled measurement streams and packet dropouts. To address the problem we propose a control structure composed of: a) a hybrid observer, which resets with the arrival of a new measurement sample; and b) a feedback of the latest estimated state and the value of the control signal computed in the previous sampling instant, generating the control to be applied to the continuous-time plant. The control signal is kept constant, by means of a zero-order hold, between two successive sampling instants. The overall closed-loop system exhibits a deterministic behavior except for jumps that occur at random sampling times resulting in a piecewise deterministic Markov process (PDMP). Using Lyapunov-based stability analysis for stochastic systems, we determine sufficient conditions for mean exponential stability (MES) of the overall closed-loop system, which are turned into Linear Matrix Inequalities (LMI) for the design of the proposed hybrid stabilizer. Finally, the effectiveness of the theoretical results is verified by an illustrative example.