Let us note that (H1s - H2s - H3s) imply (H1 - H2 - H3); hence, by using Proposition 2.4, ((x_{n})_{ninmathbb{N}}) is asymptotically regular.
Hence, by using ECF as the power source, we realize a micro inchworm robot.
Furthermore, this data space is supposed to contain all the dynamic behaviors of the system, hence, by using a basis matrix of the data space, we can establish a data-based stability condition based on the Lyapunov stability theory, which enables us to test the stability of an LTI system directly from its time series data.
Hence by using (6.20), we obtain.
Hence, by using the Arzelá-Ascoli theorem, B is compact.
Hence, by using Remark 2.4, we find that.
and, hence, by using condition (A2), we get (2.41).
Hence, by using Theorem 1, one can immediately get the desired result.
Hence by using Theorem 2.2, there exists (x^inmathcal{X}) such that (x^inmathcal{F}(x^)).
Hence, by using Danford integral and operator calculus (see, e.g., in [11]) we obtain the assertion.
Hence, by using Lemma 1, we have where is a diagonal matrix.
