Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements

Abstract

This paper is concerned with the problem of robust <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mathscr H}_{\infty }$</tex></formula> output feedback control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy affine dynamic systems using quantized measurements. The objective is to design a suitable observer-based dynamic output feedback controller that guarantees the global stability of the resulting closed-loop fuzzy system with a prescribed <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mathscr H}_{\infty }$</tex></formula> disturbance attenuation level. Based on common/piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality convexification techniques, some new results are developed to the controller synthesis for the underlying continuous-time T–S fuzzy affine systems with unmeasurable premise variables. All the solutions to the problem are formulated in the form of linear matrix inequalities (LMIs). Finally, two simulation examples are provided to illustrate the advantages of the proposed approaches.