Homogeneous Sliding Modes in Noisy Environments Avi Hanan, Adam Jbara, and Arie Levant Abstract One of the main achievements of the high-order sliding mode control (HOSMC) theory is the standardized output-feedback regulation based on the robust high-order differentiation. The method employs universal HOSM controllers valid for any relative degree combined with standard HOSM differentiators. In this chapter, we present recently developed new universal controllers and filtering differentiators and demonstrate their output-feedback application in the presence of large sampling noises. 1 Introduction Sliding mode control (SMC) [27, 53, 75, 78] has been introduced to effectively control uncertain processes. The method assumes choosing a proper system output σ called sliding variable to keep it at zero. The constraint σ ≡ 0 is to provide for the desired system performance and is established in finite time by a high-frequency switching control. The control switching is inevitable due to the uncertainty of the system. Unfor- tunately, it produces undesired system vibrations called the chattering effect [9, 15, 34, 77]. While keeping the switching, the SM control itself can be done continuous. Its discontinuity can be shifted to the higher total derivatives of the sliding variable. The number r of the first discontinuous total time derivative σ (r ) is called the SM order [44, 46]. The conventional SMs [27, 77] feature the first SM order. Higher order A. Hanan (B ) · A. Jbara · A. Levant Applied Mathematics Department, Tel-Aviv University, Tel-Aviv 6997801, Israel e-mail: avih@tauex.tau.ac.il A. Jbara e-mail: adamjbara@mail.tau.ac.il A. Levant e-mail: levant@tauex.tau.ac.il © Springer Nature Singapore Pte Ltd. 2021 A. Mehta and B. Bandyopadhyay (eds.), Emerging Trends in Sliding Mode Control, Studies in Systems, Decision and Control 318, https://doi.org/10.1007/978-981-15-8613-2_1 1