State estimation for a class of nonlinear fractional-order systems with flexRay-based protocols

This paper addresses the state estimation problem for fractional-order systems (FOS)–systems described by differential equations involving non-integer (fractional) derivatives–with nonlinear dynamics under communication constraints. To reduce communication load while effectively utilizing network resources, the FlexRay protocol (FRP), an automotive network protocol that combines time-triggered (static segment) and event-triggered (dynamic segment) communications, is incorporated into the estimator design, where its hybrid communication mechanism is explicitly exploited. A piecewise state estimation scheme is constructed using distinct scheduling rules for the static and dynamic segments. The system nonlinearity is handled under the Lipschitz condition (a mathematical condition restricting how rapidly the system’s nonlinear part can change), and the stability of the resulting estimation error system is analyzed using Lyapunov theory (a standard technique in stability analysis) and Mittag-Leffler stability criteria (a form of stability specific to fractional-order systems). By formulating the design conditions as linear matrix inequalities (LMIs, which are constraints involving matrices that must be positive definite), sufficient conditions for stability are derived, and the estimator gains are obtained analytically via the Schur complement (a method for simplifying matrix inequalities). Finally, simulation results based on an autonomous guided vehicle (AGV) tracking scenario demonstrate the effectiveness and convergence of the proposed method.