Admissible H$_\infty$ Control of Fuzzy Singular Fractional Order Multi-Agent Systems With External Disturbances

Abstract

This brief consider the problem about admissible consensus of fuzzy singular fractional order multi agent systems (FSFOMAS). By designing a new distributed fuzzy dynamic output control strategy, the coupled system achieves admissible while satisfying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> performance. Then, when the fuzzy models reduce to ordinary fractional order multi agent systems (FOMAS), a new sufficient condition for determining system consensus is given. The above results all depend only on the eigenvalues of the Laplace matrix and the state matrix of the system and consist of linear matrix inequalities (LMIs). Finally, a numerical example and a practical circuit example can demonstrate the feasibility and validity of the theorems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Due to the unique memorability of fractional orders, their application to fuzzy multi-agent systems will bring system performance metrics closer to reality. This paper investigates the stabilization of singular fuzzy fractional-order multi-agent systems with the perturbation case, the pulse case. We know that in practical applications a single variable does not accurately describe the phenomenon. Therefore we have introduced the concepts of multi-agent, fuzzy, singular and fractional orders in order to describe the system model more accurately. The main objective is to bring the system into equilibrium in the closest possible approximation to reality. The performance metrics of the system are optimised to bring the system to an optimal state. Finally, two examples are used to illustrate the validity of our theorems.