Annular Finite-Time H ₂/H ∞ Control for Mean-Field Jump-Diffusion Systems

This article addresses the annular finite-time H2/H∞ 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 H2/H∞ control is introduced, which simultaneously ensures the system's annular finite-time bounded-ness (AFTB) in the mean-square sense and the minimization of H2 and H∞ performance indices. Moreover, its superiority over finite-time H2/H∞ control is analyzed. Next, several innovative and less conservative sufficient conditions for both state feedback and observer-based annular finite-time (SFAFT and OBAFT) H2/H∞ control are proposed. Further, a new algorithm is devised. When γ is a fixed value, this algorithm can be used to obtain the range of stability parameters μ and π. When γ is a varying value, this algorithm can be employed to determine the relationship between the H2 and H∞ performance indices under different values of μ and π. Finally, a comprehensive design example is presented to showcase the practical advantages of the proposed methodologies.