This paper provides results on input-output Lp stability of networked control systems (NCSs) implemented over WirelessHART (WH). WH is a communication protocol widely used in process instrumentation. It is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We propose a non-linear hybrid model of WH-NCSs that is able to capture these network functionalities, and that it is more general than existing models in the literature. Particularly, the multi-hop nature of the network is translated into an interesting mathematical structure in our model. We then follow the emulation approach to stabilise the NCS. We first assume that we know a stabilising controller for the plant without the network. We subsequently show that, under reasonable assumptions on the scheduling protocol, stability is preserved when the controller is implemented over the network with sufficiently frequent data transmission. Specifically, we provide bounds on the maximum allowable transmission interval (MATI) under which all protocols that satisfy the property of being persistently exciting (PE) lead to Lp stable WH-NCSs. These bounds exploit the mathematical structure of our WH-NCS model, improving the existing bounds in the literature. Additionally, we explain how to schedule transmissions over the hops to satisfy the PE property. In particular, we show how simultaneous transmissions over different frequency channels can be exploited to further enlarge the MATI bound.

Abstract-We study the emulation-based stabilisation of nonlinear networked control systems (NCSs) implemented over WirelessHART (WH). WH is a communication protocol widely used in process instrumentation. It is characterised by its multi-hop structure, slotted communication cycles, and simultaneous transmission over different frequencies. To capture most functionalities of WH, faithful models are needed. We propose a hybrid control-oriented model of WH-NCSs that includes the key features of the network. We then follow an emulation approach to stabilise the NCS. We show that, under reasonable assumptions on the scheduling protocol, stability is preserved when the controller is implemented over the network with sufficiently frequent data transmission. We then explain how to schedule transmissions over the hops to satisfy those assumptions.

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