Stability Analysis and Data-Driven State Estimation for Generalized Persidskii Systems with Time Delays: Theory and Experimental Validation on PMSM Drives

A new research paper by Syed Pouladi addresses stability analysis and data-driven state estimation for a broad class of nonlinear systems with time-varying delays. The work focuses on generalized Persidskii systems, which combine linear dynamics with sector-bounded nonlinear feedback—a framework applicable to electromechanical drives and neural networks. The author develops delay-dependent input-to-state stability conditions using Lyapunov-Krasovskii functionals, then casts them as linear matrix inequalities (LMIs) for practical solver use. A structured robust observer is designed for partial-state measurement, with convergence guaranteed via an H∞ synchronization criterion. To handle unknown plant dynamics, system matrices are identified from trajectory data using a stability-preserving Koopman lifting procedure, embedding the ISS-LMI constraint as a convex side condition during regression.

The identified model populates the prediction horizon of an ICODE-MPPI (Input-dependent Control-oriented Dynamical Estimation — Model Predictive Path Integral) controller. Experimental validation on a 1.5 kW Permanent Magnet Synchronous Motor (PMSM) drive shows significant improvements: a 35% reduction in velocity estimation RMSE relative to an Extended Kalman Filter, and a 67% improvement in speed-tracking accuracy compared to standard Field-Oriented Control. The results corroborate the theoretical ISS bounds derived in the paper, demonstrating that data-driven, stability-aware observers can outperform classical methods in real-time motor control applications.