2021-03-15 Lp信号
Wang, Hanlei; Xie, Yongchun (2014). Passivity Based Attitude Control of Rigid Bodies. Asian Journal of Control, 16(3), 802–817. doi:10.1002/asjc.616
Let g(t)∈Rng(t) \in \mathcal{R}^{n}g(t)∈Rn be a function of time, and denote the norm of g(t)g(t)g(t) by ∣g(t)∣.|g(t)| .∣g(t)∣. We say g∈Lpg \in L_{p}g∈Lp? if and only if (∫0∞∣g(t)∣pdt)1p\left(\int_{0}^{\infty}|g(t)|^{p} d t\right)^{\frac{1}{p}}(∫0∞?∣g(t)∣pdt)p1? exists (i.e., (∫0∞∣g(t)∣pdt)1p\left(\int_{0}^{\infty}|g(t)|^{p} d t\right)^{\frac{1}{p}}(∫0∞?∣g(t)∣pdt)p1? is finite), where p∈[1,∞),p \in[1, \infty),p∈[1,∞), and we say g∈L∞g \in L_{\infty}g∈L∞? if and only if sup?t≥0∣g(t)∣\sup _{t \geq 0}|g(t)|supt≥0?∣g(t)∣ exists.
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