Finite-time H<inf>∞</inf>control of linear singular fractional differential equations with time-varying delay

Abstract

In this paper, we propose an efficient analytical approach based on fractional calculus and singularity value theory to designing the finite-time $H_\infty $ controller for linear singular fractional differential equations with time-varying delay. By introducing new fractional-order $H_\infty $ norm, the state feedback controller is designed to guarantee that the closed-loop system is singular, impulse-free and finite-time stable with prescribed $H_\infty $ performance. New sufficient conditions for designing the $H_\infty $ finite-time controller are presented. The results of this paper improve the corresponding ones of integer-order singular systems with time-varying delay. Finally, a numerical example demonstrates the validity and effectiveness of the proposed theoretical results.