This paper considers the problem of admissibility and admissibilization of 2D singular continuous systems described by the Roesser model. A necessary and sufficient admissibility condition is first proposed for 2D singular continuous systems in terms of a strict Linear Matrix Inequality (LMI). Then, a necessary and sufficient condition is established for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). Moreover, the stability condition is completed to give a sufficient condition to ensure a specified H_∞ disturbance attenuation level for the state feedback closed loop. To illustrate the effectiveness of the proposed methodology, a numerical example is given to illustrate an admissibilization of a state feedback closed-loop system.

This paper introduces a novel strategy for the diagnosis and fault-tolerant control (FTC) of inter-turn short-circuit (ITSC) faults in the stator windings of Doubly Fed Induction Generator (DFIG)-based wind turbines. ITSC faults are among the most common electrical issues in rotating machines: early detection is therefore essential to reduce maintenance costs and prevent severe damage to the wind turbine system. To address this, a Fault Detection and Diagnosis (FDD) approach is proposed to identify and assess the severity of ITSC faults in the stator windings. A state-space model of the DFIG under ITSC fault conditions is first developed in the (d,q) reference frame. Based on this model, an Unknown Input Observer (UIO) structured using Takagi–Sugeno (T-S) fuzzy models is designed to estimate the fault level. To mitigate the impact of the fault and ensure continued operation under degraded conditions, a T-S fuzzy fault-tolerant controller is synthesized. This controller enables natural decoupling and optimal power extraction across a wide range of rotor speed variations. Since the effectiveness of the FTC relies on accurate fault information, a Proportional-Integral Observer (PIO) is employed to estimate the ITSC fault level. The proposed diagnosis and compensation strategy is validated through simulations performed on a 3 kW wind turbine system, demonstrating its efficiency and robustness.

This paper addresses the problem of robust stabilisation of nD hybrid systems described by Roesser model. The model is in a descriptor form where all the system matrices are corrupted by uncertainty in a general form as implicit linear fractional representations . Based on the S-procedure technique, robust stability and robust stabilisation conditions are established for hybrid systems. Simulation example is provided in order to illustrate the relevance of our approach.