A Novel Approach to $H_{\bm \infty}$ Decentralized Fuzzy-Observer-Based Fuzzy Control Design for Nonlinear Interconnected Systems

Abstract

In general, due to the interactions among subsystems, it is difficult to design an <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> -decentralized output-feedback controller for nonlinear interconnected systems. This study introduces <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> -decentralized fuzzy-observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, for nonlinear interconnected systems via T-S fuzzy models. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only. A novel decoupled method is proposed in this study to transform the non-linear matrix inequality (non-LMI) conditions into some LMI forms. By the proposed decoupled method, the problem 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> -decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP) with five prespecified scalars for each subsystem. In general, it is a difficult task to solve the EVP with five prespecified scalars. Fortunately, this special EVP can be easily solved by using a genetic algorithm and an LMI-based optimization method. Finally, a simulation example is given to illustrate the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">design</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">procedure</i> and robust performance of the proposed methods.