Robust stabilization of multiplicative/relative uncertain systems and networked feedback control

Stabilization of uncertain dynamic systems is investigated focusing on plant models that involve both multiplicative and relative uncertainties that are bounded by H_¿-norm. A new notion of stability margin is proposed to study the robustness of the feedback stability. It is shown that the largest possible stability margin is a two-disk problem. An upper and lower bounds are derived which differ by only a factor of ¿2. The results are then applied to networked feedback control systems where logarithmic quantization is employed at both the plant input and output. Our results show that the coarsest quantization density can be computed based on the robust stability margin for plant models involving H_¿-norm bounded multiplicative and relative uncertainties.