Stabilization of system in Lure form over uncertain channels

In this paper, we study the problem of stabilization of nonlinear system in Lure form with uncertainty at the input and output channels. The channel uncertainty is modeled using Bernoulli random variable. Generalization of Positive Real Lemma for stochastic systems are derived to prove the main result of this paper providing sufficient condition for the mean square exponential stability of the closed loop system with erasure channels at the input and output. We generalize this result to provide sufficient condition for stabilization over general uncertain channel at the input and perfect measurement channel at the output. The results in this paper provide synthesis method for the design of controller and observer that are robust to channel uncertainty. Due to nonlinear plant dynamics, the controller and observer design problem are coupled, however we provide explicit relation between the erasure probability of the input and output channels to maintain stability of the feedback control system.