Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  address the problem of output feedback stabilization for a class of planar systems that are inherently nonlinear in the sense that the linearized system at the origin is neither controllable nor observable. Moreover, the uncontrollable modes contain eigenvalues on the right-half plane. By the ll-known necessary condition, such planar systems cannot be stabilized, even locally by any smooth output feedback, and hence must be dealt with by nonsmooth output feedback. The main contribution of this work is the development of a non-Lipschitz continuous output feedback design method that leads to a solution to the problem. The proposed output feedback control scheme is not based on the separation principle but rather, relies on the design of a reduced-order nonlinear observer from an earlier paper with an appropriate twist, and the tool of adding a por integrator. A non-Lipschitz continuous output feedback controller is explicitly constructed, achieving global stabilization of the planar systems without imposing the high-order growth conditions required in a previous paper.
['Chunjiang Qian', 'Wei Lin']
I am writing a research paper on a idea Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane
[{"from": "human", "value": "I am writing a research paper on a idea Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  address the problem of output feedback stabilization for a class of planar systems that are inherently nonlinear in the sense that the linearized system at the origin is neither controllable nor observable. Moreover, the uncontrollable modes contain eigenvalues on the right-half plane. By the ll-known necessary condition, such planar systems cannot be stabilized, even locally by any smooth output feedback, and hence must be dealt with by nonsmooth output feedback. The main contribution of this work is the development of a non-Lipschitz continuous output feedback design method that leads to a solution to the problem. The proposed output feedback control scheme is not based on the separation principle but rather, relies on the design of a reduced-order nonlinear observer from an earlier paper with an appropriate twist, and the tool of adding a por integrator. A non-Lipschitz continuous output feedback controller is explicitly constructed, achieving global stabilization of the planar systems without imposing the high-order growth conditions required in a previous paper."}]