New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals withH(infinity)control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities (LMIs) approach. Then, by introducing a new concepts of H-infinity control problem for nonlinear conformable fractional order systems, the authors study H-infinity performance analysis and H-infinity state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H-infinity performance gamma. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H-infinity performance gamma. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.