A graphical method-based Kharitonov theorem for robust stability analysis of incommensurate fractional-order uncertain systems

This paper introduces a more streamlined and convenient graphical approach to investigate the stability of fractional-order dynamical systems comprehensively. In particular, we focus on the utilization of Kharitonov theorem, renowned for robust stability analysis of incommensurate fractional-order systems in the presence of uncertainty. A novel graphical framework is illustrated, promising to streamline the stability analysis of such systems, which leads to reducing the computational burden. Using the proposed method, we can achieve the least possible Kharitonov polynomials among the existing methods to analyze the robust stability of the incommensurate fractional-order systems. To validate our approach, we perform numerical simulations on four illustrative examples, demonstrating its effectiveness. Simulation results underscore the real-world utility of our methodology, emphasizing its potential significance in fractional-order system analysis.