Quantized Fuzzy Output Feedback ${\mathcal{H}}_{\infty}$ Control for Nonlinear Systems With Adjustment of Dynamic Parameters

This paper investigates the output feedback <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> control problem for a class of continuous-time nonlinear systems with both output and input quantization. The nonlinear plant is represented by a Takagi–Sugeno fuzzy model. The measurement output and the control input signals will be quantized by dynamic quantizers. The attention of this paper is focused on the design of the output feedback controller and quantizers such that the fuzzy closed-loop system is asymptotically stable and also achieves a prescribed <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> noise attenuation level with respect to the effect of quantization. In the presence of quantization, two novel <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> performance analysis criteria are presented for the considered fuzzy systems based on the descriptor representation approach. Then, sufficient conditions for the existence of the feedback <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> controller gain and the quantizers’ dynamic parameters are expressed in terms of linear matrix inequalities. An adjusting scheme on quantizers’ parameters is proposed for the fuzzy system. Simulation examples are provided to show the effectiveness of the proposed design method.