Observer-based feedback stabilization of Lipschitz nonlinear systems in the presence of asynchronous sampling and scheduling protocols

Abstract

In this paper, the network-based observation and stabilization problems for Lipschitz nonlinear systems under scheduling communication are investigated. It is assumed that the signal transmission between the sensors and the controller or between the controller and the plant is implemented through a wireless network. Moreover, the scheduling of the sensed signal towards the controller is ruled by the Round-Robin (RR) protocol or the i.i.d. stochastic protocol. A general framework for observer-based feedback stabilization is proposed in which the control input is generated by a zero-order device which stores the sampled output of the sample-and-hold Luenberger observer-based controller. The resulting closed-loop system is modeled as a cascaded hybrid system with partial state subject to impulsive perturbation. Sufficient conditions for the existence of sample-and-hold Luenberger observer-based sampled-data controllers are derived by applying separation principle and time-dependent Lyapunov functionals. These conditions allow to design observers and controllers separately. A numerical example is presented to illustrate the effectiveness of the developed methodology.