@misc{TexisLoaizaMorenoEstradaetal., author = {Texis-Loaiza, Oscar and Moreno, Jaime A. and Estrada, Manuel A. and Fridman, Leonid and Levant, Arie}, title = {Output feedback control of nonlinear systems via Lipschitz continuous sliding modes}, series = {IEEE control systems letters}, volume = {9}, journal = {IEEE control systems letters}, publisher = {IEEE}, address = {New York, NY}, issn = {2475-1456}, doi = {10.1109/LCSYS.2025.3570982}, pages = {378 -- 383}, abstract = {This letter proposes a Lipschitz continuous output feedback sliding mode control law applicable to systems of arbitrary relative degree. The proposed controller compensates for non-vanishing perturbations with bounded time derivatives while ensuring finite-time stability of the origin. The finite-time stability of the closed-loop system is established using Lyapunov methods, leveraging the weighted homogeneity properties of both the controller and the observer. Furthermore, the observer and controller can be designed independently, thereby establishing a form of separation principle. The feasibility of the proposed method is demonstrated through simulation.}, language = {en} } @misc{TexisLoaizaEstradaFridmanetal., author = {Texis-Loaiza, Oscar and Estrada, Manuel A. and Fridman, Leonid and Moreno, Jaime A. and Levant, Arie}, title = {Output feedback control of second-order systems via Lipschitz continuous sliding modes}, series = {2024 17th International Workshop on Variable Structure Systems (VSS)}, journal = {2024 17th International Workshop on Variable Structure Systems (VSS)}, publisher = {IEEE}, address = {New York, NY}, isbn = {979-8-3503-5368-6}, issn = {1524-9050}, doi = {10.1109/VSS61690.2024.10753385}, pages = {220 -- 225}, abstract = {This paper presents an output feedback approach for second-order systems with non-vanishing perturbations. The proposed approach allows us to compensate for non-vanishing Lipschitz perturbations theoretically exactly while generating a Lipschitz continuous control signal, reducing the energy consumption by the control. To achieve such a Lipschitz continuous sliding mode control, we propose a homogeneous third-order sliding mode control law and a second-order sliding mode observer; then, we prove the finite-time stable equilibrium in a closed loop with the system. The feasibility of the result is shown through a simulation example.}, language = {en} }