Rank‐Maximal Robust Augmented Observer for Simultaneous Actuator and Sensor Fault Reconstruction in Fractional‐Order Descriptor One‐Sided Lipschitz Systems

Abstract

ABSTRACT This paper develops a rank‐maximal robust augmented observer that simultaneously reconstructs the state, the actuator faults and the sensor faults of fractional‐order descriptor (singular) systems whose nonlinearity satisfies the one‐sided Lipschitz (OSL) and quadratic inner‐boundedness (QIB) conditions. Faults are embedded into an enlarged descriptor state through a Caputo fault‐dynamics model that covers both constant and slowly time‐varying faults; the resulting estimation error is governed by an explicit (regular) fractional differential equation obtained from a general descriptor‐observer pair, the non‐uniqueness of which is exploited as a design freedom. Two consequences follow. First, the restrictive algebraic matching constraint that limits classical adaptive sensor‐fault schemes is completely removed, since the faults are reconstructed as components of the augmented state rather than through an output‐error injection. Second, an explicit rank‐maximal reconstructability condition is established: within the proposed augmented fault model, the number of faults reconstructable simultaneously is bounded by the number of independent measurements, , the bound being structurally attained whenever the plant admits a full‐column‐rank fault distribution. For constant faults the augmented error converges globally in the Mittag–Leffler sense through linear matrix inequality (LMI) conditions derived with a quadratic Lyapunov function, whereas for slowly time‐varying faults, disturbances and measurement noise a robust fractional, Riemann–Liouville‐weighted attenuation bound (an ‐type criterion that reduces to the classical induced gain only as the order tends to one) is guaranteed. The rank‐maximality claim is stated conditionally throughout: the rank tests certify structural reconstructability, while reconstruction itself additionally requires feasibility of the corresponding LMI, and an explicit plant is exhibited for which the measurement‐rank bound is structurally attained yet no feasible synthesis exists. All structural assumptions are verified by exact (finite) rank tests, the LMI feasibility certificates and the residuals of every structural identity are reported, and the method is validated on a fractional‐order descriptor benchmark and on a revisited literature example in which two sensor faults—infeasible under the matching‐constraint baseline—are reconstructed simultaneously, together with sensitivity studies in the fractional order, the OSL/QIB constants, the noise intensity and the fault‐variation rate. The main limitations are the restriction to the sub‐diffusive range , the dependence of the synthesis on globally valid and a priori known OSL/QIB constants, and the assumption of exactly known system matrices.