An Iterative LMI-Based Reduced-Order Observer Design for Fractional-Order Chaos Synchronization

In this paper, attempts are made to design a reduced-order observer for a nonlinear Lipschitz class of fractional-order systems. It is assumed that nonlinear terms not only depend on measurable states but depend on unknown states and inputs as well. The sufficient conditions for stability of the observer based on the Lyapunov technique are derived and converted into linear matrix inequalities (LMIs). To overcome the main drawback of previous research studies which assumed that the sum of terms in infinite series coming from fractional derivative of a Lyapunov function is bounded and its upper bound is predefined, we used an iterative LMI-based algorithm to find out this bound. A four-wing chaotic system is implemented in both PSpice and MATLAB software as a case study. Simulation results are reported to show the effectiveness of the proposed iterative LMI-based reduced-order observer in tracking the unmeasurable state variables of the chaotic fractional system in different initial conditions.