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Finite-time and fixed-time stabilization: implicit Lyapunov function approach. (English) Zbl 1309.93135
Summary: Theorems on Implicit Lyapunov Functions (ILF) for finite-time and fixed-time stability analysis of nonlinear systems are presented. Based on these results, new nonlinear control laws are designed for robust stabilization of a chain of integrators. High Order Sliding Mode (HOSM) algorithms are obtained as particular cases. Some aspects of digital implementations of the presented algorithms are studied, it is shown that they possess a chattering reduction ability. Theoretical results are supported by numerical simulations.

MSC:
93D21 Adaptive or robust stabilization
93D30 Lyapunov and storage functions
93B12 Variable structure systems
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