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The observer-based controller design strategy guarantees a unique globally asymptotically stable steady-state solution of the closed-loop system, which allows for unique performance evaluation in terms of disturbance attenuation.
We show that the system always admits a unique globally attractive positive equilibrium.
Then system (6.1) is uniformly persistent and has a unique globally asymptotically stable almost periodic solution.
Together with Lemma 3.3, system (1.1) has a unique globally attractive positive almost periodic solution.
Then equation (1.2) has a unique globally exponentially stable almost periodic positive solution.
Otherwise, the disease-free equilibrium is unstable and a unique globally attracting endemic equilibrium exists.
In this section, we show that there is a unique globally positive solution of system (1.2).
Then the system (4.3) has a unique globally asymptotically stable positive ω-periodic solution.
According to Theorem 3.1, system (4.1) has a unique globally attractive positive almost periodic solution.
That is to say, model (2.2) without impulsive effects has a unique globally asymptotically stable endemic equilibrium ((S_,I_, R_)).
By Theorem 5.1, system (6.1) has a unique globally asymptotically stable almost periodic solution (see Figures 2-4).
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