$$H_\infty$$ state feedback controller for power system synchronous generator modeled as singular Takagi Sugeno fuzzy with time delay

This paper presents a robust [Formula: see text] state-feedback controller design for a singular Takagi-Sugeno (T-S) fuzzy model of a synchronous generator, effectively addressing time delays, external disturbances, and algebraic constraints inherent to singular systems. The proposed controller employs a descriptor system formulation that captures both differential and algebraic equations, providing a more accurate representation of power system dynamics than conventional state-space models. Necessary and sufficient conditions for the existence of the [Formula: see text] controller are derived as strict linear matrix inequalities (LMIs), ensuring numerical tractability and guaranteeing closed-loop admissibility. The proposed controller, denoted as HITSFS (Descriptor-based [Formula: see text] control), is rigorously compared against RHITS (Non-descriptor [Formula: see text] control) and NFTSFS (Non-fragile saturation control) under exhaustive validation scenarios, including systematic parameter variations (minimum, nominal, maximum), measurement noise ([Formula: see text]-0.010 p.u.), time delays ([Formula: see text]-0.5 s), and distinct fault conditions (0.3-1.0 p.u.). The proposed HITSFS controller achieves the lowest ISE and peak overshoot across all states, with 24 total wins compared to only 2 for RHITS and 4 for NFTSFS. It demonstrates superior noise immunity (near-zero ISE for [Formula: see text]) and fault recovery, while consuming the least control energy (6.2949 pu[Formula: see text]s), consistently outperforming both baseline controllers across all test scenarios.