Robust ℋ∞ output feedback control of discrete-time networked systems with adaptive quantizers

Quantization effects are inevitable in networked control systems (NCSs). These quantization effects can be reduced by increasing the number of quantization levels. However, increasing the number of quantization levels may lead to network congestion, (i.e., the network needs to transfer more information than its capacity). In this paper, we investigate the problem of designing a robust ℋ_∞ output feedback controller for discrete-time networked systems with an adaptive quantization density or limited information. More precisely, the quantization density is designed to be a function of the network load condition which is modeled by a Markov process. A stability criterion is developed by using Lyapunov-Krasovskii functional and sufficient conditions for the existence of a dynamic quantized output feedback controller are given in terms of Bilinear Matrix Inequalities(BMIs). An iterative algorithm is suggested to obtain quasi-convex Linear Matrix Inequalities (LMIs) from BMIs. An example is presented to illustrate the effectiveness of the proposed design.