Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Any uncertain smooth single-input single-output dynamic system of the full relative degree can be locally finite-time stabilized at its equilibrium point by means of a standard continuous feedback. High-order sliding-mode approach is modified for this sake, and a list of continuous controllers is built depending only on the given relative degree n of the system output sigma. Provided the relative degree is globally ll-defined and the system growth rate is restricted, the global finite-time stabilization is possible. The asymptotic accuracies in the cases of discrete and noisy sampling are estimated. In particular, for any q > 0 the stabilization accuracy sigma  (i)  = O (zeta  n-i+q  ), i = 0, 1, ..., n - 1, is obtained, where zeta is the sampling interval, and q is an arbitrarily chosen positive feedback parameter. Output-feedback controllers are constructed. Computer simulation confirms the applicability of the approach.
['Arie Levant']
I am writing a research paper on a idea Finite-time stabilization of uncertain SISO systems
[{"from": "human", "value": "I am writing a research paper on a idea Finite-time stabilization of uncertain SISO systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Any uncertain smooth single-input single-output dynamic system of the full relative degree can be locally finite-time stabilized at its equilibrium point by means of a standard continuous feedback. High-order sliding-mode approach is modified for this sake, and a list of continuous controllers is built depending only on the given relative degree n of the system output sigma. Provided the relative degree is globally ll-defined and the system growth rate is restricted, the global finite-time stabilization is possible. The asymptotic accuracies in the cases of discrete and noisy sampling are estimated. In particular, for any q > 0 the stabilization accuracy sigma  (i)  = O (zeta  n-i+q  ), i = 0, 1, ..., n - 1, is obtained, where zeta is the sampling interval, and q is an arbitrarily chosen positive feedback parameter. Output-feedback controllers are constructed. Computer simulation confirms the applicability of the approach."}]