Control of Nonlinear Systems with Input Delays and Disturbances Using State and Disturbance Sub-Predictors

Ba Huy Nguyen (), The Dong Dang, Igor B. Furtat, Anh Quan Dao and Pavel A. Gushchin
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Ba Huy Nguyen: Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint Petersburg, Russia
The Dong Dang: Faculty of Control Systems and Robotics, ITMO University, 197101 Saint Petersburg, Russia
Igor B. Furtat: Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint Petersburg, Russia
Anh Quan Dao: Faculty of Engineering and Technology, Hung Vuong University, Viet Tri City 29000, Vietnam
Pavel A. Gushchin: Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint Petersburg, Russia

Mathematics, 2025, vol. 13, issue 11, 1-15

Abstract: This paper proposes a new method for controlling nonlinear systems with input signal delays in the presence of external disturbances. The control law consists of two components: the first component, based on a sub-predictor for the controlled variable, stabilizes the unstable system, while the second component, which is based on a disturbance sub-predictor, compensates for external disturbances. The tracking error (stabilization error), which depends on the magnitude of the disturbances, can be reduced by increasing the order of the disturbance sub-predictor. Sufficient conditions for the stability of the closed-loop system with a given maximum delay are derived using the Lyapunov–Krasovskii method and formulated as linear matrix inequalities (LMIs). Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

Keywords: nonlinear systems; delay; disturbance; controlled variable sub-predictor; disturbance sub-predictor; linear matrix inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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