Conformable switched‐gain observation for positive complex networks

This paper investigates state estimation for a class of positive complex networks (CN) described in the conformable fractional‐order framework. A centralized switched‐gain conformable observer is proposed, where the output‐injection gain switches between two predesigned modes according to a residual‐based hysteresis rule with a dwell‐time constraint. Under mild structural positivity assumptions (Metzler‐type linear part, nonnegative couplings, and nonnegative input/output channels) and a component‐wise slope bound on the nonlinear injection, we prove that the plant and observer preserve positivity and that the estimation error evolves within the nonnegative orthant under appropriate initial conditions. A comparison inequality is then established to upper bound the conformable error dynamics by a positive switched linear system. Using copositive Lyapunov arguments, we derive linear‐programming (LP) conditions that certify a conformable ‐gain bound from nonnegative disturbances to the residual signal. Numerical examples on a networked nonlinear model validate positivity preservation, switching behavior, and the certified conformable ‐gain inequality in stretched time for several conformable orders.