Theorem 3 X is a bornologic space if and only if every uniformlybounded set of linear operators from X to Y is equicontinuous.
定理3 X是囿空间的充要条件为：每个从X到Y的一致有界的线性算子族都是等度连续的。
2
It is proved that all the signals in the adaptive control system are globally uniformlybounded, and the regulation error converges to zero asymptotically.
证明了自适应控制系统的所有信号全局一致有界，调节误差渐近收敛到零。
3
Using multiple Lyapunov functions, a sufficient condition is derived to ensure that the switched nonlinear systems are uniformlybounded and uniformly ultimate bounded.