Full-State Observer Synthesis for a Class of One-Sided Lipschitz Nonlinear Fractional-Order Systems

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A full-order observer design for a large class of fractional-order continuous-time nonlinear systems that satisfies the one-sided Lipschitz and quadratic inner boundedness conditions problem is addressed. By employing the fractional-order extension of the Lyapunov direct approach, a sufficient condition for the existence of the proposed observer is established in the form of a Nonlinear Matrix Inequality (NMI), guaranteeing the asymptotic convergence of the observation error to the origin. The effectiveness and distinct advantages of the proposed design are validated through numerical simulations on a representative fractional-order system.