An LMI approach to quantized H<inf>∞</inf> control of uncertain linear systems with network-induced delays

This paper deals with a convex optimization approach to the problem of robust network-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for linear systems connected over a common digital communication network with norm-bounded parameter uncertainties. Firstly, we investigate the effect of both the output quantization levels and the network conditions under static quantizers. Secondly, by introducing a descriptor technique, using 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. One example is utilized to illustrate the design procedure proposed in this paper.