Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A unilaterally constrained perturbed double integrator system is studied in this paper. The aim is to establish uniform finite time stability of the non-linear dynamics in the presence of impacts due to the constraints on the position variable. A non-smooth transformation is utilized to first transform the system into a variable structure system that can be studied within the framework of a conventional discontinuous paradigm. Then, a finite time stable continuous controller is used and stability of the closed-loop dynamics is proven by identifying a new set of Lyapunov functions. The results enable continuous and discontinuous cases to be unified using one parameter that defines the set of Lyapunov functions for each case.
['Harshal B. Oza', 'Yury Orlov', 'Sarah K. Spurgeon']
I am writing a research paper on a idea A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets
[{"from": "human", "value": "I am writing a research paper on a idea A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A unilaterally constrained perturbed double integrator system is studied in this paper. The aim is to establish uniform finite time stability of the non-linear dynamics in the presence of impacts due to the constraints on the position variable. A non-smooth transformation is utilized to first transform the system into a variable structure system that can be studied within the framework of a conventional discontinuous paradigm. Then, a finite time stable continuous controller is used and stability of the closed-loop dynamics is proven by identifying a new set of Lyapunov functions. The results enable continuous and discontinuous cases to be unified using one parameter that defines the set of Lyapunov functions for each case."}]