Unified Riccati-Based Analysis for Robust Kalman Filter Design on Semi-Infinite Time Intervals

Abstract

Robust state estimation remains challenging under model uncertainties and time-varying dynamics, as Kalman filtering degrades when models deviate from nominal representations. The Riccati equation governs optimal control and estimation, yet classical treatments impose limiting assumptions. This article extends Sontag's theorem to time-varying systems with measurable and essentially bounded coefficients, establishing a unified framework for robust Kalman filter design on semi-infinite intervals addressing existence, uniqueness, and convergence under minimal regularity. The framework formulates robust filtering as a minimax game and employs Riccati analysis to prove global existence, convergence to a steady-state limit, and uniqueness of the optimal pair, validated through satellite attitude control simulations. Results confirm global existence, asymptotic convergence, and stability against periodic disturbances. This paper extends Sontag’s theorem on the existence and boundedness of solutions to Continuous-Time Algebraic Riccati Equations (CARE) from a finite interval  to the semi-infinite interval . The main novelty lies in establishing unified Riccati-based sufficient conditions that explicitly incorporate norm-bounded parameter uncertainties, thereby guaranteeing the asymptotic stability and  performance of the Robust Kalman Filter design over an infinite time horizon. However, the framework is limited to deterministic linear systems and excludes stochastic noise and nonlinear dynamics