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The proposed method utilizes the characteristics of almost strict positive realness (ASPR) of the controlled plant.
Soon after the notion of strict positive real (SPR) [10] was introduced (see Table 2).
The positive polar cone and strict positive polar cone of are denoted by and, respectively.
Similar Kharitonov-like results are established for the complementary sensitivity function and strict positive realness of interval systems.
Theorem 9 Let f i : R → R, i = 1, …, n, be a family of strict positive and monotone functions.
The stability of the adaptive control law is proved based on the strict positive realness, under the assumption that the plant is stable and stably invertible.
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The proposed controller is designed based on strict-positive-real (SPR) Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system.
Table S3 (Additional File 5) summarises the likelihood ratio test results for the branch test (Model H versus Model H null) and for the strict branch positive site test of positive selection (Model A versus Model A null).
For endoluminal CRBSI according to the strictest definition (positive hub culture and identical bacterial strain in blood), a 3.6-fold, non-significant, reduction was observed for patients receiving ethanol (2 of 226 versus 7 of 222; P = .103).103
In patients who classified for endoluminal CRBSI according to the strictest definition (positive hub culture with identical bacterial strain in blood), a 3.6-fold reduction was observed for patients allocated to ethanol locks (2 of 226 versus 7 of 222; P = .103).103
Let A be a unital simple separable C∗-algebra with strict comparison of positive elements.
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