Novel Frequency-Based Approach to Analyze the Stability of Polynomial Fractional Differential Equations

This paper proposes a novel approach for analyzing the stability of polynomial fractional-order systems using frequency-distributed fractional integrator model. There are two types frequency and temporal stabilization methods that global semi-global conditions attain sum-of-squares (SOS) method. Substantiation asymptotical complicated systems. According to recent studies on nonlinear systems, this concentrates with any degree nonlinearity. Global obtained (PFD) via technique employed. method can be effective in where linear matrix inequality (LMI) is incapable response. solve non-convex SOS-designed equations design framework key ideas avoid conservative problems. A Lyapunov function determined address problem PFD established sufficiently expressed conditions. The main goal article present an analytical based optimization order models form convert it into problem, by changing solution system improved.