Kernel-Based Estimation of Frequency Response Function of Strictly Passive Systems

Estimating the Frequency Response Function (FRF) of Linear Time-Invariant (LTI) systems is critical for many applications. Conventional methods often neglect physical constraints such as strict passivity–a key physical constraint that ensures energy dissipation. This paper introduces a non-parametric kernel-based method that uses prior knowledge of system passivity. The estimator is developed within a vector-valued Reproducing Kernel Hilbert Space (RKHS) framework. In this framework, the infinite-dimensional problem is reformulated as a finite-dimensional quadratic optimization problem. This formulation ensures that the estimated FRF meets strict passivity (i.e., the real part is positive) and stability. The method applies to both continuous and discrete-time systems. Integrating these physical constraints yields more robust, interpretable, and accurate FRF models, as confirmed by numerical simulations.