Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study systems in which the equilibrium point varies discontinuously according to a ll defined state or time-dependent switching law.  refer to those systems as systems with switching equilibria. To motivate our study,  describe a class of problems in engineering and biology that can be formulated using such systems.  study stability and convergence properties of those systems under various switching rules. In particular  prove convergence under arbitrary switching, time-dependent and state-dependent switching laws. In the time-dependent switching case  highlight connections beten the relaxation theorem corresponding to differential inclusions, Pulse-Width-Modulation (PWM) and averaging theory.
['Silvia Mastellone', 'Dusan M. Stipanovic', 'Mark W. Spong']
I am writing a research paper on a idea Stability and convergence for systems with switching equilibria
[{"from": "human", "value": "I am writing a research paper on a idea Stability and convergence for systems with switching equilibria"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study systems in which the equilibrium point varies discontinuously according to a ll defined state or time-dependent switching law.  refer to those systems as systems with switching equilibria. To motivate our study,  describe a class of problems in engineering and biology that can be formulated using such systems.  study stability and convergence properties of those systems under various switching rules. In particular  prove convergence under arbitrary switching, time-dependent and state-dependent switching laws. In the time-dependent switching case  highlight connections beten the relaxation theorem corresponding to differential inclusions, Pulse-Width-Modulation (PWM) and averaging theory."}]