Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    studies discrete-time invariant autonomous systems ∑: #N# x #N# #N# k  + 1 #N#  =  tf ( x #N# #N# k #N# ) y #N# #N# k #N#  =  h ( x #N# #N# k #N# )   investigate the problem of when asymptotic stability of ∑ can be characterized by means of zero-state observability of ∑ and square summability of the output function  h ( x #N# #N# k #N# ). The relationship among observability, square summable series and stability of discrete-time autonomous systems is exposed. The main result developed in this paper unifies a series of stability theorems recently proposed in the literature, and generalizes Morse's Lemma [Morse, A. S. (1990). Towards a unified theory of parameter adaptive control tunability.  IEEE Trans. Autom. Contr. ,  35 , 1002–1012.] in two directions: from continuous-time linear systems to their discrete counterparts and from linear systems to nonlinear systems.
['Wei Lin', 'Christopher I. Byrnes']
I am writing a research paper on a idea Zero-state observability and stability of discrete-time nonlinear systems
[{"from": "human", "value": "I am writing a research paper on a idea Zero-state observability and stability of discrete-time nonlinear systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    studies discrete-time invariant autonomous systems \u2211: #N# x #N# #N# k  + 1 #N#  =  tf ( x #N# #N# k #N# ) y #N# #N# k #N#  =  h ( x #N# #N# k #N# )   investigate the problem of when asymptotic stability of \u2211 can be characterized by means of zero-state observability of \u2211 and square summability of the output function  h ( x #N# #N# k #N# ). The relationship among observability, square summable series and stability of discrete-time autonomous systems is exposed. The main result developed in this paper unifies a series of stability theorems recently proposed in the literature, and generalizes Morse's Lemma [Morse, A. S. (1990). Towards a unified theory of parameter adaptive control tunability.  IEEE Trans. Autom. Contr. ,  35 , 1002\u20131012.] in two directions: from continuous-time linear systems to their discrete counterparts and from linear systems to nonlinear systems."}]