stability of nonlinear fractional order discrete-time systems for engineering applications

Data-driven approaches, by effectively capturing complex nonlinear behaviors, have emerged as a powerful tool for enhancing control of real engineering systems. nonlinear discrete-time fractional-order systems have earned much interest in the design of controllers and system modeling due to special characteristics that include long-term memory, an expansion of stability domains, and higher accuracy. it is thus very important to establish some straightforward theories for proving and analyzing stability of these particular systems. this paper represents a sophisticated approach to the stability analysis of discrete caputo fractional-order systems through the development of a new lyapunov-based stability analysis framework tailored for such systems. the effectiveness of the proposed approach has been critically analyzed theoretically and validated through numerical simulations. methodologically innovative, thus, such reasoning has provided one strong solution for the stability test problem of discrete fractional order systems, opening greater avenues toward advanced construction or progress of control theory and dynamical system theories within fractional calculus.