Discretization issues of high-order sliding modes

Abstract Uncertain high-relative-degree problems of finite-time-stable output regulation are only solvable by means of high-order sliding-mode (HOSM) controllers. Output-feedback HOSM controllers make use of robust exact differentiators also based on HOSMs. It is proved that the ultimate asymptotic accuracy of output-feedback HOSM technique is preserved, if its digital implementation in controlling continuous-time systems is based on the simple zero-order-hold control and internal one-step Euler integration. At the same time due to the integration errors there is a certain performance degradation of digital HOSM differentiators solely used for signal processing.

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