Stabilisation and improvement of performance by extension of universal formula in the presence of disturbance
Krstic-Sontag's formula proves constructively that the existence of a control Lyapunov function implies asymptotic stabilisability. A similar result can be obtained for systems subject to unknown disturbances by input-to-state stabilising control Lyapunov functions (ISS-CLFs) and the input-to-state analogue of Krstic-Sontag's formula. A generalisation of the ISS version of Krstic-Sontag's formula is provided by completely parameterising all continuous ISS control laws that can be generated from a known ISS-CLF. Given an ISS-CLF, the synthesis problem reduces to that of finding indexes b(x) and υ(x) that lead to desirable performance, i.e. convergence rate and performance index. A large family of ISS controls is shown that solve the inverse optimal gain assignment problem.
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