Robust Partially Mode Delay‐Dependent ℋ∞ Output Feedback Control of Discrete‐Time Networked Control Systems

Abstract

AbstractIn this paper, a methodology for designing an output feedback controller for discrete‐time networked control systems has been considered. More precisely, network‐induced delays between the sensor and the controller is modelled by a Markov chain with transition probabilities which are not assumed to be fully known. The systems parameter uncertainties are assumed to be norm‐bounded and possibly time‐varying. To the best of the authors knowledge, the problem of designing a partially mode delay‐dependent output feedback controller for NCSs with partially known transition probability matrix has not been investigated in the literature. Based on the Lyapunov‐Krasovskii functional approach, sufficient conditions for the existence of a robust partially mode delay‐dependent output feedback controller are given in terms of bilinear matrix inequalities which can be solved using a cone complementarity linearization algorithm. The proposed design methodology differs from the existing design methodologies in that dynamic output feedback controllers are parameterized by both modes and transition probabilities, as opposed to the existing design approaches which parameterize controllers by modes only. The results obtained reduce to the existing results on fully known transition matrices when transition probabilities are fully known. It is shown that the proposed methodology can be applied to real world systems. The proposed design methodology is verified by using a DC servo motor system where the plant and the controller are connected via a cellular network with partially known transition probability matrix.