A Blaze of Sun (A Shade of Vampire, Book 5) by Bella Forrest

By Bella Forrest

Welcome again to The Shade...

"Of path you recognize who i'm. I'm a daughter of the darkness simply as absolutely as you're his son..."

Ever for the reason that his short stumble upon with Emilia on the coloration, Derek's strategies and desires were haunted with pictures of the mysterious, appealing brunette. Plagued with guilt, he struggles to appreciate why he's so interested in this darkish stranger from his earlier.

When Emilia all of sudden looks back at the island, Derek is either terrified and intrigued. yet this time, he's made up our minds to contain Sofia and observe who this lady is.

If merely Derek and Sofia knew, Emilia is a secret that are supposed to be left undiscovered..

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Additional info for A Blaze of Sun (A Shade of Vampire, Book 5)

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12) then ˜ z(k + 1) = Az(k). 13) The following result will present an easy way to design the controller matrix gain K. 7. 11) is stable if there exist a positive definite maQ11 0 trices Q = with Q11 ∈ Rn×n , Q22 ∈ Rτ n×τ n and a matrix 0 Q22 Y ∈ Rm×n such that the following inequalities holds ¯T −Q QA¯T + I1T Y T B ¯ ¯ AQ + BY I1 −Q < 0. 14) Then, the state feedback can be chosen as K = Y Q−1 11 with which the resulting closed-loop system is stable. Proof. 11) is stable if and only if there exists positive definite matrix P such that A˜T P A˜ − P < 0.

The existence condition of a linear sliding surface for systems with mismatched uncertainties was given in [25], [26], [100], but their methods cannot be applied to systems with time-delay. In [161], a new robust stability criterion for uncertain time-delay systems is given and the SMC is proved to be applicable. There, due to use of matrix norm, the result is more or less conservative and complicated which leads to inconvenience in designing the sliding surface for uncertain time-delay systems.

0 0 .. ··· ··· .. 0 0 .. 0 0 ··· I ⎥ 0⎥ ⎥ 0⎥ ⎥ .. 8) 0⎥ ⎥ 0⎥ ⎥ .. ⎦ 0 for j = 1, 2, · · · , τ¯. 9) where σ is the piecewise constant switching signal taking value from the finite index set F = {0, 1, · · · , τ¯}. According to the theory of switched systems [172], we have the following result. 5. 1) with time-varying delay τ (k) is stable if there exists a positive definite matrix P ∈ R(¯τ +1)n×(¯τ +1)n such that the following linear inequalities hold for any i ∈ {0, 1, · · · , τ¯}: A¯Ti P A¯i − P < 0.

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