Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a generalization of the recent proposed Bessel-Legendre inequality, which is specifically derived for analyzing linear time delay systems. The proposed inequalities are able to handle almost all type of classical orthogonal polynomials such as Jacobi, Laguerre and Hermite. In utilizing Jacobi polynomials, numerous existing results can be treated as the special cases of the proposed inequalities. Furthermore,  show that it is possible to apply these inequalities simultaneously to derive lor bounds for Krasovskii functionals, thus less conservative results can be obtained. Finally, the resulting inequalities have been briefly extended to handle the systems with fast time varying delays. Two numerical examples are presented to demonstrate the effectiveness of the proposed inequalities.
['Qian Feng', 'Sing Kiong Nguang']
I am writing a research paper on a idea Orthogonal functions based integral inequalities and their applications to time delay systems
[{"from": "human", "value": "I am writing a research paper on a idea Orthogonal functions based integral inequalities and their applications to time delay systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a generalization of the recent proposed Bessel-Legendre inequality, which is specifically derived for analyzing linear time delay systems. The proposed inequalities are able to handle almost all type of classical orthogonal polynomials such as Jacobi, Laguerre and Hermite. In utilizing Jacobi polynomials, numerous existing results can be treated as the special cases of the proposed inequalities. Furthermore,  show that it is possible to apply these inequalities simultaneously to derive lor bounds for Krasovskii functionals, thus less conservative results can be obtained. Finally, the resulting inequalities have been briefly extended to handle the systems with fast time varying delays. Two numerical examples are presented to demonstrate the effectiveness of the proposed inequalities."}]