Delay-Range-Dependent Linear Matrix Inequality Approach to Quantized <i>H</i>_∞ Control of Linear Systems with Network-Induced Delays and Norm-Bounded Uncertainties

This paper deals with a convex optimization approach to the problem of robust network-based H ∞ control for linear systems connected over a common digital communication network with static quantizers. Both the polytopic and the norm-bounded uncertainties are taken into consideration separately. First, the effect of both the output quantization levels and the network conditions under static quantizers is investigated. Second, by introducing a descriptor technique, using a Lyapunov—Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities for the existence of the desired network-based quantized controllers with simultaneous consideration of network-induced delays and measurement quantization. The explicit expression of the controllers is derived to satisfy both asymptotic stability and a prescribed level of disturbance attenuation for all admissible norm-bounded uncertainties. Two examples are utilized to illustrate the design procedure proposed in this paper.