Design of [formula omitted]/passive state feedback control for delayed fractional order gene regulatory networks via new improved integral inequalities

Abstract

This work deals with H∞/passivity analysis and control design for fractional-order gene regulatory networks (FOGRNs) with delays. The results are derived by structuring a new class of Lyapunov Krasovskii functional (LKF). To deal with these LKF and time delay terms, two new fractional-order integral inequalities (FOIIs) are established. Firstly, a fractional-order free weighting matrix based integral inequality (FOFMBII) is derived. This FOFMBII includes fractional-order Wirtinger’s integral inequality (FOWII) as a particular case. Secondly, another improved FOII is constructed to facilitate the estimation of the fractional derivative of Lyapunov functional. Then, using the derived FOIIs and constructed LKF, a new set of sufficient conditions is established in terms of linear matrix inequalities (LMIs) for ensuring the stability of FOGRNs with a prescribed mixed H∞/passivity or H∞ or passivity level. The theoretical results are validated on a genetic network model. Three control gain matrices for the considered model are calculated based on H∞, passivity, and mixed H∞/passivity performances. The efficiencies of these three controllers are compared. Finally, the simulation results are given to exhibit the validity of the proposed results.