Observability of nonlinear NCS with unsynchronized sensor clocks

This paper deals with the observability of nonlinear networked control systems (NCS) with unsynchronized sensor clocks. The observability of such systems is aggravated by the loss of notion of time in a system-wide consistent manner. To overcome this problem, a suitable affine clock model with unknown parameters is introduced and the observability map of nonlinear systems with discrete-time measurements is extended accordingly. Consequently, observability is formulated in terms of full-rankness of the Jacobian of the extended observability map. This formulation is independent of the network induced packet delays but depends on the information content in the control input. For this reason, necessary conditions are derived for the control input to be sufficiently exciting. The obtained terminology and conditions are illustrated on a numerical example and the practical relevance is demonstrated on a real networked pendulum test-rig.