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The dynamic behavior of the trajectory on the surface is characterized by the solution of Filippovs differential inclusion.
By extending the elements of the state covariance matrix as augmented states, the statistical behavior of the trajectory is captured to reformulate the performance metrics and path constraints.
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Now, we study the limit behavior of the trajectories.
Besides, we study the limit behavior of the trajectories of such operators.
In this section, we study the limit behavior of the trajectories of dissipative q.s.o.o
Finally, we study the limit behavior of the trajectories of dissipative q.s.o. in Section 4.
Second, investigate the limit behavior of the trajectories for arbitrary dissipative q.s.o.o
The other three definitions are given in terms of different types of exponential behavior of the trajectories of the considered system.
It is to note that the limit behavior of the trajectories of the dissipative q.s.o. on finite-dimensional simplex (the set of vectors with non-negative components summing up to 1) was fully classified in [20].
Further development of this theory belongs to Lyubich [2, 3], Kesten [4, 5], Vallander [6], and Zakharevich [7], where the authors investigate the limit behavior of the trajectories (or dynamics) of q.s.o.o
We also studied the limit behavior of the trajectories in some particular cases that can be an impetus to further studies of dissipative q.s.o. on infinite-dimensional space.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com