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2 International Journal of Applied Mathematics and Computer Science

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On the finite time stabilization via robust control for uncertain disturbed systems

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Ordaz P. , Alazki H. , Sánchez B. , Ordaz-Oliver M.

International Journal of Applied Mathematics and Computer Science

2023

tom Vol. 33, no. 1

71--82

This paper deals with the finite-time stabilization problem for a class of uncertain disturbed systems using linear robust control. The proposed algorithm is designed to provide the robustness of a linear feedback control scheme such that system trajectories arrive at a small-size attractive set around an unstable equilibrium in a finite time. To this end, an optimization problem with a linear matrix inequality constraint is presented. This means that the effects of external disturbances, as well as matched and mismatched uncertain dynamics, can be significantly reduced. Finally, the performance of the suggested closed-loop control strategies is shown by the trajectory tracking of an unmanned aerial vehicle flight.

Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

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Ordaz P. , Romero-Trejo H. , Cuvas C. , Sandre O.

International Journal of Applied Mathematics and Computer Science

2024

tom Vol. 34, no. 1

29--43

This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.