Constrained Networked Control Systems stabilization A lambda-D-contractive set based approach
Résumé
The paper embraces the stabilization problem of Networked Control Systems 'NCSs' with a specific attention to linear dynamical systems affected by uncertain, possibly time-varying, network-induced delays in the presence of input and state constraints. Two main theoretical results are presented. First, we address the computation of a polyhedral control Lyapunov-Razumikhin Function 'pcLRF' using 1-step controllability sets. Furthermore, we show that adopting 'pcLRF' instead of quadratic control Lyapunov-Razumikhin Function 'qcLRF' reduces the conservativeness of 'LRF' based control design. Second, based on the first result, we show that polyhedral lambda-D-contractive sets can be used as a target set in a Set Induced Lyapunov Function 'SILF' control fashion where a simple Linear Programming 'LP' problem is required to be solved at each sampling instance. We prove that the proposed controller, under mild assumptions, is able to handle state/input constraints, and ensures asymptotic stability for all initial states belonging to a predefined set.