Suggest me the example systems of discrete lipschitz nonlinear systems. I want systems other than the systems which are in the form of x(k+1)=Ax(k)+f(x(k),u(k)). I want something like x(k+1)= f(x(k),u(k)).
I suggest you this paper and the references therein, which there is some examples,
Wang, D., Song, F., & Zhang, W. (2015). State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics. Advances in Difference Equations, 2015(1), 1-10.
But I have a small remark, a system like x(k+1)=Ax(k)+f(x(k),u(k)) is a special case of the general one like x(k+1)= f(x(k),u(k)).
Wang, D., Song, F., & Zhang, W. (2015). State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics. Advances in Difference Equations, 2015(1), 1-10.
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