Annular Finite-Time H₂/H∞ Control for Mean-Field Jump-Diffusion Systems

This article addresses the annular finite-time $H_{2}/H_{\infty }$ control for mean-field jump-diffusion systems (MFJDSs), where the state equation is influenced by both Wiener and Poisson noises. Initially, a new concept termed annular finite-time $H_{2}/H_{\infty }$ control is introduced, which simultaneously ensures the system's annular finite-time bounded-ness (AFTB) in the mean-square sense and the minimization of $H_{2}$ and $H_{\infty }$ performance indices. Moreover, its superiority over finite-time $H_{2}/H_{\infty }$ control is analyzed. Next, several innovative and less conservative sufficient conditions for both state feedback and observer-based annular finite-time (SFAFT and OBAFT) $H_{2}/H_{\infty }$ control are proposed. Further, a new algorithm is devised. When $ \gamma $ is a fixed value, this algorithm can be used to obtain the range of stability parameters $ \mu $ and $ \pi $ . When $\gamma $ is a varying value, this algorithm can be employed to determine the relationship between the $H_{2}$ and $H_{\infty }$ performance indices under different values of $\mu $ and $\pi $ . Finally, a comprehensive design example is presented to showcase the practical advantages of the proposed methodologies.