Non-fragile H∞ control with randomly occurring gain variations

In this paper, the non-fragile H_∞ control problem is investigated for a class of discrete-time systems with randomly occurring gain variations (ROGVs). ROGVs, which describe the new network-induced phenomenon of a controller gain appearing in a random way, are modeled by a Bernoulli distributed white sequence with a known conditional probability. We aim to analyze and design a non-fragile H_∞ output-feedback controller such that the closed-loop control system is stochastically stable while the desired H_∞ performance is guaranteed. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the stochastic stability as well as prescribed H_∞ disturbance-rejection attenuation. The controller design issue is then casted into a convex optimization one solvable by the semi-definite programme method. The effectiveness of the proposed method is demonstrated in the numerical example.