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Lucas A. L. Oliveira
Graduate Program on Mathematical and Computational Modeling (PPGMMC), CEFET-MG; CReSTIC EA3804 – Université de Reims Champagne-Ardenne, Moulin de la Housse BP1039, 51687 Reims cedex 2
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Valter J. S. Leite
Graduate Program on Mathematical and Computational Modeling (PPGMMC), CEFET-MG; Department of Mechatronics Engineering, CEFET-MG - Campus Divinópolis
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Luís F. P. Silva
Department of Mechatronics Engineering, CEFET-MG - Campus Divinópolis
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Kevin Guelton
CReSTIC EA3804 – Université de Reims Champagne-Ardenne, Moulin de la Housse BP1039, 51687 Reims cedex 2
Keywords:
Robust stabilization, Input-to-state stability, Saturating actuators, Rate saturation, Magnitude saturation, Discrete-time systems, Regional stability, Time-varying systems
Abstract
We propose new convex conditions, formulated in terms of linear matrix inequalities, allowing the design of robust state feedback controllers for time-varying discrete-time systems under saturating actuators. We consider the case where the actuators can be saturated on both magnitude and rate, which leads to more complex but realistic conditions. Because of the nonlinearities, the regional input-to-state stability is employed, handling energy-bounded disturbance signals. The feasibility of the proposed conditions allows computing safe estimates of the initial conditions sets depending on the disturbance energy. Two numerical examples illustrate the proposal’s application and serve to establish numerical comparisons with other approaches from the literature.
