Titlebook: Sliding-Mode Control and Variable-Structure Systems; The State of the Art Tiago Roux Oliveira,Leonid Fridman,Liu Hsu Book 2023 The Editor(s

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Lyapunov-Based Consistent Discretization of Quasi-continuous High-Order Sliding Modesding-mode controllers which are equipped with a homogeneous Lyapunov function. Such a Lyapunov function is used to construct the discretization scheme that preserves important features from the original continuous-time system: asymptotic stability, finite-time convergence, and the Lyapunov function

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Describing Function-Based Analysis and Design of Approximated Sliding-Mode Controllers with Reduced matched bounded disturbances and finite-time convergence. However, the insensitivity requires an ideal implementation of discontinuous signals, often based on the sign function that, in practice, results in the presence of parasitic oscillations called chattering. Chattering is unavoidable in system

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On Finite- and Fixed-Time State Estimation for Uncertain Linear Systemste-time and fixed-time convergence properties and the synthesis of these observers are described along this chapter. Moreover, an unknown input identification approach is also introduced. Simulation results illustrate the performance of these state estimation approaches.

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