Stability and H∞ Control of Systems with Variable Quantization Density in Both Input and Output Channels

This paper is concerned with the problems of stability analysis and Hoo control for a class of systems with quantized signals in both control input channel and measurement output channel. The quantization density of each quantizer is considered to be variable, and the variations of the quantizers are governed by a Markov chain. With the aid of quantization-error-dependent Lyapunov function approach, a set of Hoo controllers depending on the mode of quantization density are carried out to achieve the stochastic stability and the prescribed Hoo performance of the closed-loop system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control method and the benefits of the variability of quantization density.