Control of systems in Lure form over erasure channels

In this paper, we study the problem of control of discrete-time nonlinear systems in Lure form over erasure channels at the input and output. The input and output channel uncertainties are modeled as Bernoulli random variables. The main results of this paper provide sufficient condition for the mean square exponential stability of the closed loop system expressed in terms of statistics of channel uncertainty and plant characteristics. We also provide synthesis method for the design of observer-based controller that is robust to channel uncertainty. To prove the main results of this paper, we discover a stochastic variant of the well known Positive Real Lemma and principle of separation for stochastic nonlinear system. Application of the results for the stabilization of system in Lure form over packet-drop network is discussed. Finally a result for state feedback control of a Lure system with a general multiplicative uncertainty at actuation is discussed.