Stability analysis of networked control systems with direct-feedthrough terms: part I : The nonlinear case

This paper investigates the stability of nonlinear networked control systems (NCSs) with dynamic controllers that possess direct-feedthrough terms (i.e. that are of relative degree zero). The presence of the direct-feedthrough terms obstructs the application of existing stability results for NCSs. Indeed, the uniform global exponential stability (UGES) of an auxiliary system induced by the plant and the network protocol needs to be verified. In prior work, this auxiliary system depends solely on the protocol (and not on the plant or on the controller) and, consequently, the analysis is simpler. Checking UGES of this auxiliary system turns out to be nontrivial when direct-feedthrough terms are present (even for the simplest protocols). Still, we are able to show UGES of the auxiliary system for Round-Robin (RR) and Try-Once-Discard (TOD) network protocols, which, together with other requirements on the maximum allowable transmission intervals (MATIs), ensures the stability of the overall system. We also show that the analysis and proofs can be greatly simplified in cases when the control inputs are sent over one communication channel and the plant outputs over a separate channel