Reliable $H_{\infty}$ Nonuniform Sampling Fuzzy Control for Nonlinear Systems With Time Delay

Abstract

The problem of reliable <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> nonuniform sampling fuzzy control for nonlinear systems with time delay is investigated in this paper. Utilizing the input delay approach and the descriptor model transformation, an equivalent continuous-time generalized Takagi-Sugeno fuzzy system is obtained. Sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee the requirements of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance criterion for the normal and possible actuator fault cases. In order to relax the conservatism of these obtained conditions, a feasible algorithm is provided to remove some slightly restricted conditions in LMIs. Finally, an illustrative example is given to show the validity of the proposed scheme.