consider a r-integrator chain
\dot z_1 = z_2
...
\dot z_r = \phi + \gamma u.
where \gamma is bounded positive (to ensure the controlability), and the TIME DERIVATIVE of \phi and \gamma are also bounded. contrary to problem formulation of HOSM where \phi is assumed to be bounded, not its time derivative.
I'm looking for a controller u which ensure r+1 sliding mode and can be called r-order supertwisting.
Does aneyone have a bibliography of such controller u, where u is continuous or quasicontinuous?
YOU may carefully read the paper of LEVANT 1993. "SLIDING MODE, SLIDING ORDER AND SLIDING ACCURACY"
Thank you Imran,
this is a novel field of research in sliding mode ...
Below a preprint to our approch for Higher Order Supertwisting (continuous and quasicontinuous cases).
https://www.researchgate.net/publication/280590093_Higher_order_supertwisting_algorithm_for_perturbed_chains_of_integrators_of_arbitrary_order
Regards
Article Higher order supertwisting algorithm for perturbed chains of...
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