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arXiv · 2509.04090

Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances

Egor Dogadin·Alexey Peregudin
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Abstract

This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an integral-based measure of their size. To minimize this measure, we develop a differential Riccati equation-based approach that provides exact solutions for state-feedback, observer synthesis, and output-feedback control. A key component is a systematic procedure for determining the optimal time-varying parameter, reducing an infinite-dimensional optimization to a simple iterative process. A numerical example validates the method's effectiveness.

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Egor Dogadin, Alexey Peregudin. 2025-09-04. Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances. https://doi.org/10.1109/lcsys.2025.3570559

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